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Resolución de integrales/ x^(2)/ (5*x^(5)+8)/ (3*x^(2)+2*x)/(5*x^(5)+8)

Integral de (3*x^(2)+2*x)/(5*x^(5)+8) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo              
  /              
 |               
 |     2         
 |  3*x  + 2*x   
 |  ---------- dx
 |      5        
 |   5*x  + 8    
 |               
/                
2
∫2∞3x2+2x5x5+8 dx\int\limits_{2}^{\infty} \frac{3 x^{2} + 2 x}{5 x^{5} + 8}\, dx 
Integral((3*x^2 + 2*x)/(5*x^5 + 8), (x, 2, oo))
Solución detallada

  1. Hay varias maneras de calcular esta integral.

    Método #1

    1. Vuelva a escribir el integrando:

      3x2+2x5x5+8=x(3x+2)5x5+8\frac{3 x^{2} + 2 x}{5 x^{5} + 8} = \frac{x \left(3 x + 2\right)}{5 x^{5} + 8}

    2. Vuelva a escribir el integrando:

      x(3x+2)5x5+8=3x25x5+8+2x5x5+8\frac{x \left(3 x + 2\right)}{5 x^{5} + 8} = \frac{3 x^{2}}{5 x^{5} + 8} + \frac{2 x}{5 x^{5} + 8}

    3. Integramos término a término:

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

        ∫3x25x5+8 dx=3∫x25x5+8 dx\int \frac{3 x^{2}}{5 x^{5} + 8}\, dx = 3 \int \frac{x^{2}}{5 x^{5} + 8}\, dx

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

          Pero la integral

          RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))\operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)}

        Por lo tanto, el resultado es: 3RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))3 \operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)}

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

        ∫2x5x5+8 dx=2∫x5x5+8 dx\int \frac{2 x}{5 x^{5} + 8}\, dx = 2 \int \frac{x}{5 x^{5} + 8}\, dx

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

          Pero la integral

          RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))\operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

        Por lo tanto, el resultado es: 2RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))2 \operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

      El resultado es: 3RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))+2RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))3 \operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

    Método #2

    1. Vuelva a escribir el integrando:

      3x2+2x5x5+8=3x25x5+8+2x5x5+8\frac{3 x^{2} + 2 x}{5 x^{5} + 8} = \frac{3 x^{2}}{5 x^{5} + 8} + \frac{2 x}{5 x^{5} + 8}

    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:

        ∫3x25x5+8 dx=3∫x25x5+8 dx\int \frac{3 x^{2}}{5 x^{5} + 8}\, dx = 3 \int \frac{x^{2}}{5 x^{5} + 8}\, dx

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

          Pero la integral

          RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))\operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)}

        Por lo tanto, el resultado es: 3RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))3 \operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)}

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

        ∫2x5x5+8 dx=2∫x5x5+8 dx\int \frac{2 x}{5 x^{5} + 8}\, dx = 2 \int \frac{x}{5 x^{5} + 8}\, dx

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

          Pero la integral

          RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))\operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

        Por lo tanto, el resultado es: 2RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))2 \operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

      El resultado es: 3RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))+2RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))3 \operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}

  2. Ahora simplificar:

    3⋅2025log⁡(x+500055)100+3(−2025400+245⋅5910400−2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400−2025i58+58100)2)+3(−2025400+245⋅5910400+2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400+2025i58+58100)2)+2(2505400+5710505400+2505i58−58100)log⁡(x−40000(2505400+5710505400+2505i58−58100)3)+3(−245⋅5910400−2025400−2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400−2025i58−58100)2)+3(−245⋅5910400−2025400+2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400+2025i58−58100)2)+2(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)log⁡(x−40000(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)3)+2(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)log⁡(x−40000(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)3)+2(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)log⁡(x−40000(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)3)+2(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)log⁡(x−40000(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)3)\frac{3 \cdot 20^{\frac{2}{5}} \log{\left(x + \frac{\sqrt[5]{5000}}{5} \right)}}{100} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 2 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x - 40000 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{3} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 2 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right)^{3} \right)}

  3. Añadimos la constante de integración:

    3⋅2025log⁡(x+500055)100+3(−2025400+245⋅5910400−2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400−2025i58+58100)2)+3(−2025400+245⋅5910400+2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400+2025i58+58100)2)+2(2505400+5710505400+2505i58−58100)log⁡(x−40000(2505400+5710505400+2505i58−58100)3)+3(−245⋅5910400−2025400−2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400−2025i58−58100)2)+3(−245⋅5910400−2025400+2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400+2025i58−58100)2)+2(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)log⁡(x−40000(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)3)+2(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)log⁡(x−40000(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)3)+2(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)log⁡(x−40000(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)3)+2(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)log⁡(x−40000(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)3)+constant\frac{3 \cdot 20^{\frac{2}{5}} \log{\left(x + \frac{\sqrt[5]{5000}}{5} \right)}}{100} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 2 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x - 40000 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{3} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 2 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right)^{3} \right)}+ \mathrm{constant}

Respuesta:

3⋅2025log⁡(x+500055)100+3(−2025400+245⋅5910400−2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400−2025i58+58100)2)+3(−2025400+245⋅5910400+2025i58+58100)log⁡(x+1000(−2025400+245⋅5910400+2025i58+58100)2)+2(2505400+5710505400+2505i58−58100)log⁡(x−40000(2505400+5710505400+2505i58−58100)3)+3(−245⋅5910400−2025400−2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400−2025i58−58100)2)+3(−245⋅5910400−2025400+2025i58−58100)log⁡(x+1000(−245⋅5910400−2025400+2025i58−58100)2)+2(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)log⁡(x−40000(−1125051600−25⋅535320−25510320−105⋅59101600+5710505800−105⋅5910i58−58400+25510i58−5880)3)+2(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)log⁡(x−40000(−25⋅535320−5710505800−25510320−105⋅59101600+925051600−25510i58−5880−105⋅5910i58−58400−2505i58−58200)3)+2(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)log⁡(x−40000(−25510320−25051600+105⋅59101600+25⋅535320+250558−5858+58100−25510i58+5880−2505i58+58400−2505i58−58400+105⋅5910i58−58400)3)+2(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)log⁡(x−40000(−250558−5858+58100−25510320−25051600+105⋅59101600+25⋅535320−2505i58−58400+2505i58+58400+105⋅5910i58−58400+25510i58+5880)3)+constant\frac{3 \cdot 20^{\frac{2}{5}} \log{\left(x + \frac{\sqrt[5]{5000}}{5} \right)}}{100} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{20^{\frac{2}{5}}}{400} + \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100}\right)^{2} \right)} + 2 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x - 40000 \left(\frac{\sqrt[5]{250}}{400} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{3} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} - \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 3 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right) \log{\left(x + 1000 \left(- \frac{2^{\frac{4}{5}} \cdot 5^{\frac{9}{10}}}{400} - \frac{20^{\frac{2}{5}}}{400} + \frac{20^{\frac{2}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100}\right)^{2} \right)} + 2 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{11 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{5^{\frac{7}{10}} \sqrt[5]{50}}{800} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{9 \sqrt[5]{250}}{1600} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{80} - \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{200}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} + \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80} - \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400}\right)^{3} \right)} + 2 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right) \log{\left(x - 40000 \left(- \frac{\sqrt[5]{250} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} - \frac{\sqrt[5]{2} \sqrt[10]{5}}{320} - \frac{\sqrt[5]{250}}{1600} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}}}{1600} + \frac{\sqrt[5]{2} \cdot 5^{\frac{3}{5}}}{320} - \frac{\sqrt[5]{250} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{250} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{400} + \frac{\sqrt[5]{10} \cdot 5^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{400} + \frac{\sqrt[5]{2} \sqrt[10]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{80}\right)^{3} \right)}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
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 |    2                                                                                                                          
 | 3*x  + 2*x                   /          5                /           3\\            /          5                /          2\\
 | ---------- dx = C + 2*RootSum\40000000*t  + 1, t -> t*log\x - 40000*t // + 3*RootSum\25000000*t  - 1, t -> t*log\x + 1000*t //
 |     5                                                                                                                         
 |  5*x  + 8                                                                                                                     
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∫3x2+2x5x5+8 dx=C+3RootSum⁡(25000000t5−1,(t↦tlog⁡(1000t2+x)))+2RootSum⁡(40000000t5+1,(t↦tlog⁡(−40000t3+x)))\int \frac{3 x^{2} + 2 x}{5 x^{5} + 8}\, dx = C + 3 \operatorname{RootSum} {\left(25000000 t^{5} - 1, \left( t \mapsto t \log{\left(1000 t^{2} + x \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(40000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 40000 t^{3} + x \right)} \right)\right)}
Simplificar
Gráfica
2.00002.01002.00102.00202.00302.00402.00502.00602.00702.00802.00900.2-0.2
Trazar el gráfico f(x)

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

    © Sr Examen – Калькулятор