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Resolución de integrales/ x^5+1/ 1/(x^5+1)

Integral de 1/(x^5+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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∫011x5+1 dx\int\limits_{0}^{1} \frac{1}{x^{5} + 1}\, dx 
Integral(1/(x^5 + 1), (x, 0, 1))
Solución detallada

  1. Vuelva a escribir el integrando:

    1x5+1=−x3−2x2+3x−45(x4−x3+x2−x+1)+15(x+1)\frac{1}{x^{5} + 1} = - \frac{x^{3} - 2 x^{2} + 3 x - 4}{5 \left(x^{4} - x^{3} + x^{2} - x + 1\right)} + \frac{1}{5 \left(x + 1\right)}

  2. Integramos término a término:

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      ∫(−x3−2x2+3x−45(x4−x3+x2−x+1)) dx=−∫x3−2x2+3x−4x4−x3+x2−x+1 dx5\int \left(- \frac{x^{3} - 2 x^{2} + 3 x - 4}{5 \left(x^{4} - x^{3} + x^{2} - x + 1\right)}\right)\, dx = - \frac{\int \frac{x^{3} - 2 x^{2} + 3 x - 4}{x^{4} - x^{3} + x^{2} - x + 1}\, dx}{5}

      1. Vuelva a escribir el integrando:

        x3−2x2+3x−4x4−x3+x2−x+1=x3x4−x3+x2−x+1−2x2x4−x3+x2−x+1+3xx4−x3+x2−x+1−4x4−x3+x2−x+1\frac{x^{3} - 2 x^{2} + 3 x - 4}{x^{4} - x^{3} + x^{2} - x + 1} = \frac{x^{3}}{x^{4} - x^{3} + x^{2} - x + 1} - \frac{2 x^{2}}{x^{4} - x^{3} + x^{2} - x + 1} + \frac{3 x}{x^{4} - x^{3} + x^{2} - x + 1} - \frac{4}{x^{4} - x^{3} + x^{2} - x + 1}

      2. Integramos término a término:

        1. No puedo encontrar los pasos en la búsqueda de esta integral.

          Pero la integral

          (520+14)log⁡(x2+x(−1158−98−105+316+1525+316)−37105+364−3525+364+958+7116)+(14−520)log⁡(x2+x(−1523−516−98−103−516+1158)−958−37103−564+3523−564+7116)−2−103−5200+120atan⁡(−32x10−103−5+10+253−5−103−5+10+32−103−5+10−22510−103−5+10+253−5−103−5+10+32−103−5+10+103−510−103−5+10+253−5−103−5+10+32−103−5+10+1810−103−5+10+253−5−103−5+10+32−103−5+10+1523−510−103−5+10+253−5−103−5+10+32−103−5+10)+2−105+3200+120atan⁡(−32x−255+3−105+3+10−32−105+3+10+10−105+3+10+225−255+3−105+3+10−32−105+3+10+10−105+3+10+18−255+3−105+3+10−32−105+3+10+10−105+3+10+105+3−255+3−105+3+10−32−105+3+10+10−105+3+10−1525+3−255+3−105+3+10−32−105+3+10+10−105+3+10)\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)} + \left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)} - 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)}

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          ∫(−2x2x4−x3+x2−x+1) dx=−2∫x2x4−x3+x2−x+1 dx\int \left(- \frac{2 x^{2}}{x^{4} - x^{3} + x^{2} - x + 1}\right)\, dx = - 2 \int \frac{x^{2}}{x^{4} - x^{3} + x^{2} - x + 1}\, dx

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

            5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)10−5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)10+2−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)+2−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)\frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{10} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{10} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}

          Por lo tanto, el resultado es: −5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)5+5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)5−4−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)−4−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)- \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{5} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{5} - 4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} - 4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          ∫3xx4−x3+x2−x+1 dx=3∫xx4−x3+x2−x+1 dx\int \frac{3 x}{x^{4} - x^{3} + x^{2} - x + 1}\, dx = 3 \int \frac{x}{x^{4} - x^{3} + x^{2} - x + 1}\, dx

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

            −2110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)−2550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)- 2 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)} - 2 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}

          Por lo tanto, el resultado es: −6110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)−6550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)- 6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)} - 6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}

        1. La integral del producto de una función por una constante es la constante por la integral de esta función:

          ∫(−4x4−x3+x2−x+1) dx=−4∫1x4−x3+x2−x+1 dx\int \left(- \frac{4}{x^{4} - x^{3} + x^{2} - x + 1}\right)\, dx = - 4 \int \frac{1}{x^{4} - x^{3} + x^{2} - x + 1}\, dx

          1. No puedo encontrar los pasos en la búsqueda de esta integral.

            Pero la integral

            5log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)10−5log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)10+2−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)+2−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)\frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{10} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{10} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}

          Por lo tanto, el resultado es: −25log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)5+25log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)5−8−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)−8−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)- \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{5} + \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{5} - 8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} - 8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}

        El resultado es: −25log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)5+25log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)5−5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)5+(520+14)log⁡(x2+x(−1158−98−105+316+1525+316)−37105+364−3525+364+958+7116)+(14−520)log⁡(x2+x(−1523−516−98−103−516+1158)−958−37103−564+3523−564+7116)+5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)5−6110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)−6550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)−2−103−5200+120atan⁡(−32x10−103−5+10+253−5−103−5+10+32−103−5+10−22510−103−5+10+253−5−103−5+10+32−103−5+10+103−510−103−5+10+253−5−103−5+10+32−103−5+10+1810−103−5+10+253−5−103−5+10+32−103−5+10+1523−510−103−5+10+253−5−103−5+10+32−103−5+10)−8−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)−4−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)−8−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)+2−105+3200+120atan⁡(−32x−255+3−105+3+10−32−105+3+10+10−105+3+10+225−255+3−105+3+10−32−105+3+10+10−105+3+10+18−255+3−105+3+10−32−105+3+10+10−105+3+10+105+3−255+3−105+3+10−32−105+3+10+10−105+3+10−1525+3−255+3−105+3+10−32−105+3+10+10−105+3+10)−4−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)- \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{5} + \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{5} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{5} + \left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)} + \left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{5} - 6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)} - 6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)} - 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)} - 8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} - 4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} - 8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)} - 4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}

      Por lo tanto, el resultado es: 25log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)25−25log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)25+5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)25−(520+14)log⁡(x2+x(−1158−98−105+316+1525+316)−37105+364−3525+364+958+7116)5−(14−520)log⁡(x2+x(−1523−516−98−103−516+1158)−958−37103−564+3523−564+7116)5−5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)25+6110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)5+6550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)5+2−103−5200+120atan⁡(−32x10−103−5+10+253−5−103−5+10+32−103−5+10−22510−103−5+10+253−5−103−5+10+32−103−5+10+103−510−103−5+10+253−5−103−5+10+32−103−5+10+1810−103−5+10+253−5−103−5+10+32−103−5+10+1523−510−103−5+10+253−5−103−5+10+32−103−5+10)5+8−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)5+4−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)5+8−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)5−2−105+3200+120atan⁡(−32x−255+3−105+3+10−32−105+3+10+10−105+3+10+225−255+3−105+3+10−32−105+3+10+10−105+3+10+18−255+3−105+3+10−32−105+3+10+10−105+3+10+105+3−255+3−105+3+10−32−105+3+10+10−105+3+10−1525+3−255+3−105+3+10−32−105+3+10+10−105+3+10)5+4−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)5\frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{5} - \frac{\left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{5} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)}}{5} + \frac{6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}}{5} + \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5} - \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5}

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      ∫15(x+1) dx=∫1x+1 dx5\int \frac{1}{5 \left(x + 1\right)}\, dx = \frac{\int \frac{1}{x + 1}\, dx}{5}

      1. que u=x+1u = x + 1.

        Luego que du=dxdu = dx y ponemos dudu:

        ∫1u du\int \frac{1}{u}\, du

        1. Integral 1u\frac{1}{u} es log⁡(u)\log{\left(u \right)}.

        Si ahora sustituir uu más en:

        log⁡(x+1)\log{\left(x + 1 \right)}

      Por lo tanto, el resultado es: log⁡(x+1)5\frac{\log{\left(x + 1 \right)}}{5}

    El resultado es: log⁡(x+1)5+25log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)25−25log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)25+5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)25−(520+14)log⁡(x2+x(−1158−98−105+316+1525+316)−37105+364−3525+364+958+7116)5−(14−520)log⁡(x2+x(−1523−516−98−103−516+1158)−958−37103−564+3523−564+7116)5−5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)25+6110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)5+6550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)5+2−103−5200+120atan⁡(−32x10−103−5+10+253−5−103−5+10+32−103−5+10−22510−103−5+10+253−5−103−5+10+32−103−5+10+103−510−103−5+10+253−5−103−5+10+32−103−5+10+1810−103−5+10+253−5−103−5+10+32−103−5+10+1523−510−103−5+10+253−5−103−5+10+32−103−5+10)5+8−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)5+4−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)5+8−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)5−2−105+3200+120atan⁡(−32x−255+3−105+3+10−32−105+3+10+10−105+3+10+225−255+3−105+3+10−32−105+3+10+10−105+3+10+18−255+3−105+3+10−32−105+3+10+10−105+3+10+105+3−255+3−105+3+10−32−105+3+10+10−105+3+10−1525+3−255+3−105+3+10−32−105+3+10+10−105+3+10)5+4−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)5\frac{\log{\left(x + 1 \right)}}{5} + \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{5} - \frac{\left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{5} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)}}{5} + \frac{6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}}{5} + \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5} - \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5}

  3. Ahora simplificar:

    log⁡(x+1)5+5log⁡(x2+x(−925−6103−5+7523−5+94)22−42875242−3929103−5484+464523−5484+12387242)25−25log⁡(x2−x(−425−8103−5+4523−5+96)22−22135242−1381103−5484+304523−5484+5217242)25−(5−5)log⁡(x2−x(−225+103−5+18+1523−5)16−958−37103−564+3523−564+7116)100−5log⁡(x2+x(−7525+3−6105+3+94+925)22−3929105+3484−464525+3484+42875242+12387242)25+25log⁡(x2−x(−4525+3−8105+3+425+96)22−1381105+3484−304525+3484+22135242+5217242)25−(5+5)log⁡(x2−x(−1525+3+105+3+18+225)16−37105+364−3525+364+958+7116)100+325+5atan⁡(−42x+2+10(−1+5)5+5)25+325−5atan⁡(42x−2+10(1+5)5−5)25+4−2103−5+15atan⁡(44x−96−4523−5+8103−5+425−2103−5+15(−85+3103−5+18))25+2−2103−5+15atan⁡(44x−925−6103−5+7523−5+94−2103−5+15(−65+8+5103−5))25+2−103−5+10atan⁡(−32x−225+103−5+18+1523−5−103−5+10(10+253−5+32))50+2−2105+3+15atan⁡(44x−7525+3−6105+3+94+925−2105+3+15(8+65+5105+3))25+4−2105+3+15atan⁡(44x−96−425+8105+3+4525+3−2105+3+15(85+18+3105+3))25+2−105+3+10atan⁡(−32x−1525+3+105+3+18+225−105+3+10(−10+32+255+3))50\frac{\log{\left(x + 1 \right)}}{5} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94\right)}{22} - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 42 \sqrt{5} - 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 96\right)}{22} - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} - \frac{\left(5 - \sqrt{5}\right) \log{\left(x^{2} - \frac{x \left(- 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}\right)}{16} - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{100} - \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}\right)}{22} - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 45 \sqrt{2} \sqrt{\sqrt{5} + 3} - 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 \sqrt{5} + 96\right)}{22} - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{\left(\sqrt{5} + 5\right) \log{\left(x^{2} - \frac{x \left(- 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}\right)}{16} - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{100} + \frac{3 \sqrt{2} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{- 4 \sqrt{2} x + \sqrt{2} + \sqrt{10}}{\left(-1 + \sqrt{5}\right) \sqrt{\sqrt{5} + 5}} \right)}}{25} + \frac{3 \sqrt{2} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x - \sqrt{2} + \sqrt{10}}{\left(1 + \sqrt{5}\right) \sqrt{5 - \sqrt{5}}} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 42 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 8 \sqrt{5} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} + 18\right)} \right)}}{25} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 6 \sqrt{5} + 8 + 5 \sqrt{10} \sqrt{3 - \sqrt{5}}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \operatorname{atan}{\left(\frac{- 32 x - 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \left(\sqrt{10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} + 3 \sqrt{2}\right)} \right)}}{50} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 + 6 \sqrt{5} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 42 \sqrt{5} + 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 \sqrt{5} + 18 + 3 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \operatorname{atan}{\left(\frac{- 32 x - 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}}{\sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \left(- \sqrt{10} + 3 \sqrt{2} + 2 \sqrt{5} \sqrt{\sqrt{5} + 3}\right)} \right)}}{50}

  4. Añadimos la constante de integración:

    log⁡(x+1)5+5log⁡(x2+x(−925−6103−5+7523−5+94)22−42875242−3929103−5484+464523−5484+12387242)25−25log⁡(x2−x(−425−8103−5+4523−5+96)22−22135242−1381103−5484+304523−5484+5217242)25−(5−5)log⁡(x2−x(−225+103−5+18+1523−5)16−958−37103−564+3523−564+7116)100−5log⁡(x2+x(−7525+3−6105+3+94+925)22−3929105+3484−464525+3484+42875242+12387242)25+25log⁡(x2−x(−4525+3−8105+3+425+96)22−1381105+3484−304525+3484+22135242+5217242)25−(5+5)log⁡(x2−x(−1525+3+105+3+18+225)16−37105+364−3525+364+958+7116)100+325+5atan⁡(−42x+2+10(−1+5)5+5)25+325−5atan⁡(42x−2+10(1+5)5−5)25+4−2103−5+15atan⁡(44x−96−4523−5+8103−5+425−2103−5+15(−85+3103−5+18))25+2−2103−5+15atan⁡(44x−925−6103−5+7523−5+94−2103−5+15(−65+8+5103−5))25+2−103−5+10atan⁡(−32x−225+103−5+18+1523−5−103−5+10(10+253−5+32))50+2−2105+3+15atan⁡(44x−7525+3−6105+3+94+925−2105+3+15(8+65+5105+3))25+4−2105+3+15atan⁡(44x−96−425+8105+3+4525+3−2105+3+15(85+18+3105+3))25+2−105+3+10atan⁡(−32x−1525+3+105+3+18+225−105+3+10(−10+32+255+3))50+constant\frac{\log{\left(x + 1 \right)}}{5} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94\right)}{22} - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 42 \sqrt{5} - 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 96\right)}{22} - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} - \frac{\left(5 - \sqrt{5}\right) \log{\left(x^{2} - \frac{x \left(- 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}\right)}{16} - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{100} - \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}\right)}{22} - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 45 \sqrt{2} \sqrt{\sqrt{5} + 3} - 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 \sqrt{5} + 96\right)}{22} - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{\left(\sqrt{5} + 5\right) \log{\left(x^{2} - \frac{x \left(- 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}\right)}{16} - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{100} + \frac{3 \sqrt{2} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{- 4 \sqrt{2} x + \sqrt{2} + \sqrt{10}}{\left(-1 + \sqrt{5}\right) \sqrt{\sqrt{5} + 5}} \right)}}{25} + \frac{3 \sqrt{2} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x - \sqrt{2} + \sqrt{10}}{\left(1 + \sqrt{5}\right) \sqrt{5 - \sqrt{5}}} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 42 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 8 \sqrt{5} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} + 18\right)} \right)}}{25} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 6 \sqrt{5} + 8 + 5 \sqrt{10} \sqrt{3 - \sqrt{5}}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \operatorname{atan}{\left(\frac{- 32 x - 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \left(\sqrt{10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} + 3 \sqrt{2}\right)} \right)}}{50} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 + 6 \sqrt{5} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 42 \sqrt{5} + 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 \sqrt{5} + 18 + 3 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \operatorname{atan}{\left(\frac{- 32 x - 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}}{\sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \left(- \sqrt{10} + 3 \sqrt{2} + 2 \sqrt{5} \sqrt{\sqrt{5} + 3}\right)} \right)}}{50}+ \mathrm{constant}

Respuesta:

log⁡(x+1)5+5log⁡(x2+x(−925−6103−5+7523−5+94)22−42875242−3929103−5484+464523−5484+12387242)25−25log⁡(x2−x(−425−8103−5+4523−5+96)22−22135242−1381103−5484+304523−5484+5217242)25−(5−5)log⁡(x2−x(−225+103−5+18+1523−5)16−958−37103−564+3523−564+7116)100−5log⁡(x2+x(−7525+3−6105+3+94+925)22−3929105+3484−464525+3484+42875242+12387242)25+25log⁡(x2−x(−4525+3−8105+3+425+96)22−1381105+3484−304525+3484+22135242+5217242)25−(5+5)log⁡(x2−x(−1525+3+105+3+18+225)16−37105+364−3525+364+958+7116)100+325+5atan⁡(−42x+2+10(−1+5)5+5)25+325−5atan⁡(42x−2+10(1+5)5−5)25+4−2103−5+15atan⁡(44x−96−4523−5+8103−5+425−2103−5+15(−85+3103−5+18))25+2−2103−5+15atan⁡(44x−925−6103−5+7523−5+94−2103−5+15(−65+8+5103−5))25+2−103−5+10atan⁡(−32x−225+103−5+18+1523−5−103−5+10(10+253−5+32))50+2−2105+3+15atan⁡(44x−7525+3−6105+3+94+925−2105+3+15(8+65+5105+3))25+4−2105+3+15atan⁡(44x−96−425+8105+3+4525+3−2105+3+15(85+18+3105+3))25+2−105+3+10atan⁡(−32x−1525+3+105+3+18+225−105+3+10(−10+32+255+3))50+constant\frac{\log{\left(x + 1 \right)}}{5} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94\right)}{22} - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 42 \sqrt{5} - 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 96\right)}{22} - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} - \frac{\left(5 - \sqrt{5}\right) \log{\left(x^{2} - \frac{x \left(- 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}\right)}{16} - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{100} - \frac{\sqrt{5} \log{\left(x^{2} + \frac{x \left(- 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}\right)}{22} - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{2 \sqrt{5} \log{\left(x^{2} - \frac{x \left(- 45 \sqrt{2} \sqrt{\sqrt{5} + 3} - 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 \sqrt{5} + 96\right)}{22} - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{\left(\sqrt{5} + 5\right) \log{\left(x^{2} - \frac{x \left(- 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}\right)}{16} - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{100} + \frac{3 \sqrt{2} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{- 4 \sqrt{2} x + \sqrt{2} + \sqrt{10}}{\left(-1 + \sqrt{5}\right) \sqrt{\sqrt{5} + 5}} \right)}}{25} + \frac{3 \sqrt{2} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x - \sqrt{2} + \sqrt{10}}{\left(1 + \sqrt{5}\right) \sqrt{5 - \sqrt{5}}} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 45 \sqrt{2} \sqrt{3 - \sqrt{5}} + 8 \sqrt{10} \sqrt{3 - \sqrt{5}} + 42 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 8 \sqrt{5} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} + 18\right)} \right)}}{25} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \operatorname{atan}{\left(\frac{44 x - 92 \sqrt{5} - 6 \sqrt{10} \sqrt{3 - \sqrt{5}} + 75 \sqrt{2} \sqrt{3 - \sqrt{5}} + 94}{\sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} \left(- 6 \sqrt{5} + 8 + 5 \sqrt{10} \sqrt{3 - \sqrt{5}}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \operatorname{atan}{\left(\frac{- 32 x - 22 \sqrt{5} + \sqrt{10} \sqrt{3 - \sqrt{5}} + 18 + 15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} \left(\sqrt{10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} + 3 \sqrt{2}\right)} \right)}}{50} + \frac{2 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 75 \sqrt{2} \sqrt{\sqrt{5} + 3} - 6 \sqrt{10} \sqrt{\sqrt{5} + 3} + 94 + 92 \sqrt{5}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 + 6 \sqrt{5} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{4 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \operatorname{atan}{\left(\frac{44 x - 96 - 42 \sqrt{5} + 8 \sqrt{10} \sqrt{\sqrt{5} + 3} + 45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{\sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} \left(8 \sqrt{5} + 18 + 3 \sqrt{10} \sqrt{\sqrt{5} + 3}\right)} \right)}}{25} + \frac{\sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \operatorname{atan}{\left(\frac{- 32 x - 15 \sqrt{2} \sqrt{\sqrt{5} + 3} + \sqrt{10} \sqrt{\sqrt{5} + 3} + 18 + 22 \sqrt{5}}{\sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} \left(- \sqrt{10} + 3 \sqrt{2} + 2 \sqrt{5} \sqrt{\sqrt{5} + 3}\right)} \right)}}{50}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                                        ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           ____________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
                                       /                ___________      /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ___________                                                                                                                                     ___________                                                           \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                ___________      /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ___________                                                                                                                                     ___________                                                           \                                                                                                                                                                                   /                ___________      /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ___________                                                                                                                                      ___________                                                            \          /                ___________      /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ___________                                                                                                                                      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          ___                                                                                                                                  ____   /       ___                                                                                                                               ___   /       ___                                                            |                                                                                                                                                                                  /         ____   /       ___       |                                                                                                                                                                                                                                                                                                                                                                          ___                                                                                                                                      ___   /       ___                                                                                                                               ____   /       ___                                                             |         /         ____   /       ___       |                                                                                                                                                                                                                         ___                                                                                                                                                                                                                                                                                      ____   /       ___                                                                                                                                ___   /       ___                                                             |          ____________                                                                                                                                      ____________                                                                                                                                           /         ____   /       ___       |                                                                                                                                                                                                                             ___                                                                                                                                                                                                                                                                                        ____   /       ___                                                                                                                                 ___   /       ___                                                             |         /         ____   /       ___       |                                                                                                                                                                                                                             ___                                                                                                                                                                                                                                                                                         ___   /       ___                                                                                                                                ____   /       ___                                                             |
                                     /   1    \/ 10 *\/  3 + \/ 5        |                                                                     18                                                                                                                                            32*x                                                                                                                                         22*\/ 5                                                                                                                                 \/ 10 *\/  3 + \/ 5                                                                                                                           15*\/ 2 *\/  3 + \/ 5                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               /   1    \/ 10 *\/  3 - \/ 5        |                                                                     18                                                                                                                                            32*x                                                                                                                                         22*\/ 5                                                                                                                                 \/ 10 *\/  3 - \/ 5                                                                                                                           15*\/ 2 *\/  3 - \/ 5                                                             |                                                                                                                                                                                 /   3    \/ 10 *\/  3 + \/ 5        |                                                                      94                                                                                                                                              44*x                                                                                                                                           92*\/ 5                                                                                                                                  75*\/ 2 *\/  3 + \/ 5                                                                                                                            6*\/ 10 *\/  3 + \/ 5                                                              |        /   3    \/ 10 *\/  3 - \/ 5        |                                                                      94                                                                                                                                            92*\/ 5                                                                                                                                            44*x                                                                                                                                   6*\/ 10 *\/  3 - \/ 5                                                                                                                            75*\/ 2 *\/  3 - \/ 5                                                              |         /        ___      /                  ____                                    ___                                       ___              \         /        ___      /                   ___                                       ____                                        ___               \        /   3    \/ 10 *\/  3 + \/ 5        |                                                                         96                                                                                                                                             42*\/ 5                                                                                                                                             44*x                                                                                                                                    8*\/ 10 *\/  3 + \/ 5                                                                                                                             45*\/ 2 *\/  3 + \/ 5                                                              |        /   3    \/ 10 *\/  3 - \/ 5        |                                                                         96                                                                                                                                             42*\/ 5                                                                                                                                             44*x                                                                                                                                    45*\/ 2 *\/  3 - \/ 5                                                                                                                             8*\/ 10 *\/  3 - \/ 5                                                              |
                                2*  /    -- - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|              /                           /                              ___________               ___________\                  ___________                 ___________\                  /                      /                             ___________             ___________\                ___________               ___________\                  /                      /                           ___________               ___________\                ___________               ___________\            /                            /                            ___________               ___________\                 ___________                  ___________\            /                            /                            ___________               ___________\                  ___________                 ___________\   2*  /    -- - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------|              /                           /                              ___________               ___________\                 ___________                  ___________\   4*  /    -- - --------------------- *atan|---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------|   4*  /    -- - --------------------- *atan|---------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------|        /  1    \/ 5       |                \/ 10                                   \/ 2                                  4*x*\/ 2               |        /  1    \/ 5       |                 \/ 2                                      \/ 10                                   4*x*\/ 2                |   8*  /    -- - --------------------- *atan|- ----------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------|   8*  /    -- - --------------------- *atan|- ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------|
                                  \/     20            200               |           ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________|              |                   ___     |            ___        ___   /       ___        ____   /       ___ |          ____   /       ___           ___   /       ___ |   /      ___\    |              ___     |           ___        ___   /       ___      ____   /       ___ |        ____   /       ___         ___   /       ___ |   /      ___\    |              ___     |           ___     ____   /       ___         ___   /       ___ |        ____   /       ___         ___   /       ___ |            |                    ___     |          ___        ___   /       ___        ____   /       ___ |          ___   /       ___           ____   /       ___ |            |                    ___     |          ___       ____   /       ___         ___   /       ___ |          ____   /       ___           ___   /       ___ |     \/     20            200               |           ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________              ____________________________               ____________________________                              ____________________________|              |                   ___     |            ___       ____   /       ___         ___   /       ___ |          ___   /       ___           ____   /       ___ |     \/     20             50               |      ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________|     \/     20             50               |      ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________         ______________________________               ______________________________                               ______________________________|   6*  /   -- - ----- *atan|------------------------------------- - ------------------------------------- + -------------------------------------|   6*  /   -- + ----- *atan|--------------------------------------- + --------------------------------------- - ---------------------------------------|     \/     20             50               |         ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________|     \/     20             50               |         ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________          ______________________________               ______________________________                               ______________________________|
  /                                                                      |          /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________ |       ___    |5217    2   2213*\/ 5      |  48   21*\/ 5    45*\/ 2 *\/  3 - \/ 5     4*\/ 10 *\/  3 - \/ 5  |   1381*\/ 10 *\/  3 - \/ 5     3045*\/ 2 *\/  3 - \/ 5  |   |1   \/ 5 |    |71    2   9*\/ 5      |  9   11*\/ 5    15*\/ 2 *\/  3 - \/ 5     \/ 10 *\/  3 - \/ 5  |   37*\/ 10 *\/  3 - \/ 5     35*\/ 2 *\/  3 - \/ 5  |   |1   \/ 5 |    |71    2   9*\/ 5      |  9   11*\/ 5    \/ 10 *\/  3 + \/ 5     15*\/ 2 *\/  3 + \/ 5  |   37*\/ 10 *\/  3 + \/ 5     35*\/ 2 *\/  3 + \/ 5  |     ___    |12387    2   4287*\/ 5      |47   46*\/ 5    75*\/ 2 *\/  3 + \/ 5     3*\/ 10 *\/  3 + \/ 5  |   4645*\/ 2 *\/  3 + \/ 5     3929*\/ 10 *\/  3 + \/ 5  |     ___    |12387    2   4287*\/ 5      |47   46*\/ 5    3*\/ 10 *\/  3 - \/ 5     75*\/ 2 *\/  3 - \/ 5  |   3929*\/ 10 *\/  3 - \/ 5     4645*\/ 2 *\/  3 - \/ 5  |                                            |          /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________              /                ___________               /                ___________               ___________    /                ___________ |       ___    |5217    2   2213*\/ 5      |  48   21*\/ 5    4*\/ 10 *\/  3 + \/ 5     45*\/ 2 *\/  3 + \/ 5  |   3045*\/ 2 *\/  3 + \/ 5     1381*\/ 10 *\/  3 + \/ 5  |                                            |     /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________ |                                            |     /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________         /                  ___________               /                  ___________                ___________    /                  ___________ |     \/    10     50       |   ___________            ___________      ___________            ___________      ___________            ___________|     \/    10     50       |     ___________            ___________        ___________            ___________        ___________            ___________|                                            |        /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________ |                                            |        /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________          /                  ___________               /                  ___________                ___________    /                  ___________ |
 |                                                                       |  ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___  |   2*\/ 5 *log|---- + x  - ---------- + x*|- -- + -------- - ----------------------- + -----------------------| - -------------------------- + -------------------------|   |- - -----|*log|-- + x  - ------- + x*|- - + -------- - ----------------------- - ---------------------| - ------------------------ + -----------------------|   |- + -----|*log|-- + x  + ------- + x*|- - - -------- - --------------------- + -----------------------| - ------------------------ - -----------------------|   \/ 5 *log|----- + x  + ---------- + x*|-- + -------- - ----------------------- - -----------------------| - ------------------------- - --------------------------|   \/ 5 *log|----- + x  - ---------- + x*|-- - -------- - ----------------------- + -----------------------| - -------------------------- + -------------------------|                                            |  ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___       ____   /         ____   /       ___         ___   /         ____   /       ___         ___   /       ___    /         ____   /       ___  |   2*\/ 5 *log|---- + x  + ---------- + x*|- -- - -------- + ----------------------- + -----------------------| - ------------------------- - --------------------------|                                            |    /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                                            |    /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___         /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                           |  /       ___      ___   /       ___      /       ___      ___   /       ___      /       ___      ___   /       ___ |                           |    /       ___      ___   /       ___        /       ___      ___   /       ___        /       ___      ___   /       ___ |                                            |       /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |                                            |       /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___          /           ____   /       ___         ___   /           ____   /       ___         ____   /       ___    /           ____   /       ___  |
 |   1             log(1 + x)                                            \\/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 + \/ 5    - 3*\/ 2 *\/   10 - \/ 10 *\/  3 + \/ 5    - 2*\/ 5 *\/  3 + \/ 5  *\/   10 - \/ 10 *\/  3 + \/ 5   /              \242            242         \  11      11                 22                        11          /              484                          484           /   \4     20 /    \16           8        \  8      8                  16                       16         /              64                         64          /   \4     20 /    \16           8        \  8      8                 16                       16          /              64                         64          /            \ 242            242         \11      11                 22                        11          /              484                         484            /            \ 242            242         \11      11                 11                        22          /              484                          484           /                                            \\/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5      \/ 10 *\/   10 - \/ 10 *\/  3 - \/ 5    + 3*\/ 2 *\/   10 - \/ 10 *\/  3 - \/ 5    + 2*\/ 5 *\/  3 - \/ 5  *\/   10 - \/ 10 *\/  3 - \/ 5   /              \242            242         \  11      11                 11                        22          /              484                         484            /                                            \8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      8*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 5*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5   /                                            \8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      8*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 6*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 5*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5   /                           \\/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5     \/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5     \/  5 - \/ 5   + \/ 5 *\/  5 - \/ 5  /                           \- \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5     - \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5     - \/  5 + \/ 5   + \/ 5 *\/  5 + \/ 5  /                                            \  18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5      18*\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 + \/ 5    + 3*\/ 10 *\/  3 + \/ 5  *\/   15 - 2*\/ 10 *\/  3 + \/ 5   /                                            \  18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5      18*\/   15 - 2*\/ 10 *\/  3 - \/ 5    - 8*\/ 5 *\/   15 - 2*\/ 10 *\/  3 - \/ 5    + 3*\/ 10 *\/  3 - \/ 5  *\/   15 - 2*\/ 10 *\/  3 - \/ 5   /
 | ------ dx = C + ---------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |  5                  5                                                                                                                                                                                                                                                                                                                                                                                                 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              25                                                                                                                                                                   5                                                                                                                                                                5                                                                                                                                                                   25                                                                                                                                                                    25                                                                                                                                                                                                                                                                                                                                                                                                                                                                            5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              25                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               5                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5                                                                                                                                                    5                                                                                                                                                                                                                                                                                                                                                                                                                                                                              5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      5                                                                                                                                                                                                                                                                                                                                                                                                  
 | x  + 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
/
∫1x5+1 dx=C+log⁡(x+1)5+25log⁡(x2+x(−4811−21511+4105+311+4525+322)−1381105+3484−304525+3484+22135242+5217242)25−25log⁡(x2+x(−4811−4523−522+4103−511+21511)−22135242−1381103−5484+304523−5484+5217242)25+5log⁡(x2+x(−46511−3103−511+7523−522+4711)−42875242−3929103−5484+464523−5484+12387242)25−(520+14)log⁡(x2+x(−1158−98−105+316+1525+316)−37105+364−3525+364+958+7116)5−(14−520)log⁡(x2+x(−1523−516−98−103−516+1158)−958−37103−564+3523−564+7116)5−5log⁡(x2+x(−7525+322−3105+311+4711+46511)−3929105+3484−464525+3484+42875242+12387242)25+6110−550atan⁡(42x5−5+55−5−25−5+55−5+105−5+55−5)5+6550+110atan⁡(−42x−5+5+55+5+2−5+5+55+5+10−5+5+55+5)5+2−103−5200+120atan⁡(−32x10−103−5+10+253−5−103−5+10+32−103−5+10−22510−103−5+10+253−5−103−5+10+32−103−5+10+103−510−103−5+10+253−5−103−5+10+32−103−5+10+1810−103−5+10+253−5−103−5+10+32−103−5+10+1523−510−103−5+10+253−5−103−5+10+32−103−5+10)5+8−103−550+320atan⁡(44x−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−96−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15−4523−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+8103−5−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15+425−85−2103−5+15+3103−5−2103−5+15+18−2103−5+15)5+4−103−550+320atan⁡(44x−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−925−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15−6103−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+7523−5−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15+94−65−2103−5+15+8−2103−5+15+5103−5−2103−5+15)5+8−105+350+320atan⁡(44x85−2105+3+15+18−2105+3+15+3105+3−2105+3+15−9685−2105+3+15+18−2105+3+15+3105+3−2105+3+15−42585−2105+3+15+18−2105+3+15+3105+3−2105+3+15+8105+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15+4525+385−2105+3+15+18−2105+3+15+3105+3−2105+3+15)5−2−105+3200+120atan⁡(−32x−255+3−105+3+10−32−105+3+10+10−105+3+10+225−255+3−105+3+10−32−105+3+10+10−105+3+10+18−255+3−105+3+10−32−105+3+10+10−105+3+10+105+3−255+3−105+3+10−32−105+3+10+10−105+3+10−1525+3−255+3−105+3+10−32−105+3+10+10−105+3+10)5+4−105+350+320atan⁡(44x8−2105+3+15+65−2105+3+15+5105+3−2105+3+15−7525+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15−6105+38−2105+3+15+65−2105+3+15+5105+3−2105+3+15+948−2105+3+15+65−2105+3+15+5105+3−2105+3+15+9258−2105+3+15+65−2105+3+15+5105+3−2105+3+15)5\int \frac{1}{x^{5} + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{5} + \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{25} - \frac{2 \sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{25} + \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{46 \sqrt{5}}{11} - \frac{3 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{47}{11}\right) - \frac{4287 \sqrt{5}}{242} - \frac{3929 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{4645 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{12387}{242} \right)}}{25} - \frac{\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x^{2} + x \left(- \frac{11 \sqrt{5}}{8} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{16} + \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{16}\right) - \frac{37 \sqrt{10} \sqrt{\sqrt{5} + 3}}{64} - \frac{35 \sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{9 \sqrt{5}}{8} + \frac{71}{16} \right)}}{5} - \frac{\left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x^{2} + x \left(- \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{16} - \frac{9}{8} - \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{16} + \frac{11 \sqrt{5}}{8}\right) - \frac{9 \sqrt{5}}{8} - \frac{37 \sqrt{10} \sqrt{3 - \sqrt{5}}}{64} + \frac{35 \sqrt{2} \sqrt{3 - \sqrt{5}}}{64} + \frac{71}{16} \right)}}{5} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{47}{11} + \frac{46 \sqrt{5}}{11}\right) - \frac{3929 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{4645 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{4287 \sqrt{5}}{242} + \frac{12387}{242} \right)}}{25} + \frac{6 \sqrt{\frac{1}{10} - \frac{\sqrt{5}}{50}} \operatorname{atan}{\left(\frac{4 \sqrt{2} x}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} - \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{\sqrt{5 - \sqrt{5}} + \sqrt{5} \sqrt{5 - \sqrt{5}}} \right)}}{5} + \frac{6 \sqrt{\frac{\sqrt{5}}{50} + \frac{1}{10}} \operatorname{atan}{\left(- \frac{4 \sqrt{2} x}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{10}}{- \sqrt{\sqrt{5} + 5} + \sqrt{5} \sqrt{\sqrt{5} + 5}} \right)}}{5} + \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} - \frac{22 \sqrt{5}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{18}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} + \frac{15 \sqrt{2} \sqrt{3 - \sqrt{5}}}{\sqrt{10} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 2 \sqrt{5} \sqrt{3 - \sqrt{5}} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10} + 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{3 - \sqrt{5}} + 10}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{92 \sqrt{5}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{6 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{75 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{94}{- 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 8 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 5 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)}}{5} + \frac{8 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5} - \frac{2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{200} + \frac{1}{20}} \operatorname{atan}{\left(- \frac{32 x}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{22 \sqrt{5}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{18}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} - \frac{15 \sqrt{2} \sqrt{\sqrt{5} + 3}}{- 2 \sqrt{5} \sqrt{\sqrt{5} + 3} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} - 3 \sqrt{2} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10} + \sqrt{10} \sqrt{- \sqrt{10} \sqrt{\sqrt{5} + 3} + 10}} \right)}}{5} + \frac{4 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{75 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{6 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{94}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{92 \sqrt{5}}{8 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 6 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 5 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}}{5}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
         /     4        3       2                           \   log(2)          /     4        3       2                               \
- RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(1 + 5*t)/
                                                                  5
−RootSum⁡(625t4+125t3+25t2+5t+1,(t↦tlog⁡(5t)))+RootSum⁡(625t4+125t3+25t2+5t+1,(t↦tlog⁡(5t+1)))+log⁡(2)5- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5} 
=
= 
         /     4        3       2                           \   log(2)          /     4        3       2                               \
- RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t  + 125*t  + 25*t  + 5*t + 1, t -> t*log(1 + 5*t)/
                                                                  5
−RootSum⁡(625t4+125t3+25t2+5t+1,(t↦tlog⁡(5t)))+RootSum⁡(625t4+125t3+25t2+5t+1,(t↦tlog⁡(5t+1)))+log⁡(2)5- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5} 
-RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(5*_t))) + log(2)/5 + RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(1 + 5*_t)))
Respuesta numérica [src] 
0.888313572651789
0.888313572651789

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор