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Resolución de integrales/ x^2+1/ 2*x^4/ 1*x^2/ x^4/(2*x^4+11*x^2+13)^2

Integral de x^4/(2*x^4+11*x^2+13)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |            4            
 |           x             
 |  -------------------- dx
 |                     2   
 |  /   4       2     \    
 |  \2*x  + 11*x  + 13/    
 |                         
/                          
0
∫01x4((2x4+11x2)+13)2 dx\int\limits_{0}^{1} \frac{x^{4}}{\left(\left(2 x^{4} + 11 x^{2}\right) + 13\right)^{2}}\, dx 
Integral(x^4/(2*x^4 + 11*x^2 + 13)^2, (x, 0, 1))
Solución detallada

  1. Hay varias maneras de calcular esta integral.

    Método #1

    1. Vuelva a escribir el integrando:

      x4((2x4+11x2)+13)2=−11x2+132(2x4+11x2+13)2+12(2x4+11x2+13)\frac{x^{4}}{\left(\left(2 x^{4} + 11 x^{2}\right) + 13\right)^{2}} = - \frac{11 x^{2} + 13}{2 \left(2 x^{4} + 11 x^{2} + 13\right)^{2}} + \frac{1}{2 \left(2 x^{4} + 11 x^{2} + 13\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:

        ∫(−11x2+132(2x4+11x2+13)2) dx=−∫11x2+13(2x4+11x2+13)2 dx2\int \left(- \frac{11 x^{2} + 13}{2 \left(2 x^{4} + 11 x^{2} + 13\right)^{2}}\right)\, dx = - \frac{\int \frac{11 x^{2} + 13}{\left(2 x^{4} + 11 x^{2} + 13\right)^{2}}\, dx}{2}

        1. Vuelva a escribir el integrando:

          11x2+13(2x4+11x2+13)2=11x2+134x8+44x6+173x4+286x2+169\frac{11 x^{2} + 13}{\left(2 x^{4} + 11 x^{2} + 13\right)^{2}} = \frac{11 x^{2} + 13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}

        2. Vuelva a escribir el integrando:

          11x2+134x8+44x6+173x4+286x2+169=11x24x8+44x6+173x4+286x2+169+134x8+44x6+173x4+286x2+169\frac{11 x^{2} + 13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169} = \frac{11 x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169} + \frac{13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}

        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:

            ∫11x24x8+44x6+173x4+286x2+169 dx=11∫x24x8+44x6+173x4+286x2+169 dx\int \frac{11 x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx = 11 \int \frac{x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx

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

              Pero la integral

              −4x3+11x68x4+374x2+442−247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{4 x^{3} + 11 x}{68 x^{4} + 374 x^{2} + 442} - 2 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 2 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

            Por lo tanto, el resultado es: −11(4x3+11x)68x4+374x2+442−2247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−2217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{11 \left(4 x^{3} + 11 x\right)}{68 x^{4} + 374 x^{2} + 442} - 22 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 22 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

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

            ∫134x8+44x6+173x4+286x2+169 dx=13∫14x8+44x6+173x4+286x2+169 dx\int \frac{13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx = 13 \int \frac{1}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx

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

              Pero la integral

              22x3+69x884x4+4862x2+5746+21131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+288121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)\frac{22 x^{3} + 69 x}{884 x^{4} + 4862 x^{2} + 5746} + 2 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 2 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)}

            Por lo tanto, el resultado es: 13(22x3+69x)884x4+4862x2+5746+261131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+2688121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)\frac{13 \left(22 x^{3} + 69 x\right)}{884 x^{4} + 4862 x^{2} + 5746} + 26 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 26 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)}

          El resultado es: −11(4x3+11x)68x4+374x2+442+13(22x3+69x)884x4+4862x2+5746−2247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)+261131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+2688121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)−2217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{11 \left(4 x^{3} + 11 x\right)}{68 x^{4} + 374 x^{2} + 442} + \frac{13 \left(22 x^{3} + 69 x\right)}{884 x^{4} + 4862 x^{2} + 5746} - 22 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} + 26 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 26 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} - 22 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

        Por lo tanto, el resultado es: 11(4x3+11x)2(68x4+374x2+442)−13(22x3+69x)2(884x4+4862x2+5746)+1147632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−131131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)−1388121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)+1117120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)\frac{11 \left(4 x^{3} + 11 x\right)}{2 \left(68 x^{4} + 374 x^{2} + 442\right)} - \frac{13 \left(22 x^{3} + 69 x\right)}{2 \left(884 x^{4} + 4862 x^{2} + 5746\right)} + 11 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 13 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} - 13 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} + 11 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

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

        ∫12(2x4+11x2+13) dx=∫12x4+11x2+13 dx2\int \frac{1}{2 \left(2 x^{4} + 11 x^{2} + 13\right)}\, dx = \frac{\int \frac{1}{2 x^{4} + 11 x^{2} + 13}\, dx}{2}

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

          Pero la integral

          −2111768−171768atan⁡(426x1711−17+1111−17)−2171768+111768atan⁡(426x−1117+11+1717+11)- 2 \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} - 2 \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)}

        Por lo tanto, el resultado es: −111768−171768atan⁡(426x1711−17+1111−17)−171768+111768atan⁡(426x−1117+11+1717+11)- \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} - \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)}

      El resultado es: 11(4x3+11x)2(68x4+374x2+442)−13(22x3+69x)2(884x4+4862x2+5746)−111768−171768atan⁡(426x1711−17+1111−17)+1147632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−131131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)−1388121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)−171768+111768atan⁡(426x−1117+11+1717+11)+1117120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)\frac{11 \left(4 x^{3} + 11 x\right)}{2 \left(68 x^{4} + 374 x^{2} + 442\right)} - \frac{13 \left(22 x^{3} + 69 x\right)}{2 \left(884 x^{4} + 4862 x^{2} + 5746\right)} - \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} + 11 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 13 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} - 13 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} - \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)} + 11 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

    Método #2

    1. Vuelva a escribir el integrando:

      x4((2x4+11x2)+13)2=x44x8+44x6+173x4+286x2+169\frac{x^{4}}{\left(\left(2 x^{4} + 11 x^{2}\right) + 13\right)^{2}} = \frac{x^{4}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}

    2. Vuelva a escribir el integrando:

      x44x8+44x6+173x4+286x2+169=−11x2+132(2x4+11x2+13)2+12(2x4+11x2+13)\frac{x^{4}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169} = - \frac{11 x^{2} + 13}{2 \left(2 x^{4} + 11 x^{2} + 13\right)^{2}} + \frac{1}{2 \left(2 x^{4} + 11 x^{2} + 13\right)}

    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:

        ∫(−11x2+132(2x4+11x2+13)2) dx=−∫11x2+13(2x4+11x2+13)2 dx2\int \left(- \frac{11 x^{2} + 13}{2 \left(2 x^{4} + 11 x^{2} + 13\right)^{2}}\right)\, dx = - \frac{\int \frac{11 x^{2} + 13}{\left(2 x^{4} + 11 x^{2} + 13\right)^{2}}\, dx}{2}

        1. Vuelva a escribir el integrando:

          11x2+13(2x4+11x2+13)2=11x2+134x8+44x6+173x4+286x2+169\frac{11 x^{2} + 13}{\left(2 x^{4} + 11 x^{2} + 13\right)^{2}} = \frac{11 x^{2} + 13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}

        2. Vuelva a escribir el integrando:

          11x2+134x8+44x6+173x4+286x2+169=11x24x8+44x6+173x4+286x2+169+134x8+44x6+173x4+286x2+169\frac{11 x^{2} + 13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169} = \frac{11 x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169} + \frac{13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}

        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:

            ∫11x24x8+44x6+173x4+286x2+169 dx=11∫x24x8+44x6+173x4+286x2+169 dx\int \frac{11 x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx = 11 \int \frac{x^{2}}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx

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

              Pero la integral

              −4x3+11x68x4+374x2+442−247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{4 x^{3} + 11 x}{68 x^{4} + 374 x^{2} + 442} - 2 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 2 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

            Por lo tanto, el resultado es: −11(4x3+11x)68x4+374x2+442−2247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−2217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{11 \left(4 x^{3} + 11 x\right)}{68 x^{4} + 374 x^{2} + 442} - 22 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 22 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

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

            ∫134x8+44x6+173x4+286x2+169 dx=13∫14x8+44x6+173x4+286x2+169 dx\int \frac{13}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx = 13 \int \frac{1}{4 x^{8} + 44 x^{6} + 173 x^{4} + 286 x^{2} + 169}\, dx

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

              Pero la integral

              22x3+69x884x4+4862x2+5746+21131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+288121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)\frac{22 x^{3} + 69 x}{884 x^{4} + 4862 x^{2} + 5746} + 2 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 2 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)}

            Por lo tanto, el resultado es: 13(22x3+69x)884x4+4862x2+5746+261131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+2688121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)\frac{13 \left(22 x^{3} + 69 x\right)}{884 x^{4} + 4862 x^{2} + 5746} + 26 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 26 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)}

          El resultado es: −11(4x3+11x)68x4+374x2+442+13(22x3+69x)884x4+4862x2+5746−2247632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)+261131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)+2688121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)−2217120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)- \frac{11 \left(4 x^{3} + 11 x\right)}{68 x^{4} + 374 x^{2} + 442} + \frac{13 \left(22 x^{3} + 69 x\right)}{884 x^{4} + 4862 x^{2} + 5746} - 22 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} + 26 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} + 26 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} - 22 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

        Por lo tanto, el resultado es: 11(4x3+11x)2(68x4+374x2+442)−13(22x3+69x)2(884x4+4862x2+5746)+1147632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−131131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)−1388121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)+1117120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)\frac{11 \left(4 x^{3} + 11 x\right)}{2 \left(68 x^{4} + 374 x^{2} + 442\right)} - \frac{13 \left(22 x^{3} + 69 x\right)}{2 \left(884 x^{4} + 4862 x^{2} + 5746\right)} + 11 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 13 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} - 13 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} + 11 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

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

        ∫12(2x4+11x2+13) dx=∫12x4+11x2+13 dx2\int \frac{1}{2 \left(2 x^{4} + 11 x^{2} + 13\right)}\, dx = \frac{\int \frac{1}{2 x^{4} + 11 x^{2} + 13}\, dx}{2}

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

          Pero la integral

          −2111768−171768atan⁡(426x1711−17+1111−17)−2171768+111768atan⁡(426x−1117+11+1717+11)- 2 \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} - 2 \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)}

        Por lo tanto, el resultado es: −111768−171768atan⁡(426x1711−17+1111−17)−171768+111768atan⁡(426x−1117+11+1717+11)- \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} - \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)}

      El resultado es: 11(4x3+11x)2(68x4+374x2+442)−13(22x3+69x)2(884x4+4862x2+5746)−111768−171768atan⁡(426x1711−17+1111−17)+1147632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−131131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)−1388121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)−171768+111768atan⁡(426x−1117+11+1717+11)+1117120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)\frac{11 \left(4 x^{3} + 11 x\right)}{2 \left(68 x^{4} + 374 x^{2} + 442\right)} - \frac{13 \left(22 x^{3} + 69 x\right)}{2 \left(884 x^{4} + 4862 x^{2} + 5746\right)} - \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} + 11 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 13 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} - 13 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} - \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)} + 11 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}

  2. Ahora simplificar:

    4862x(4x2+11)−442x(22x2+69)+442(2x4+11x2+13)(−88121−192117atan⁡(3442426x(−957+3517)88121−192117)+111717+4763atan⁡(186826x(−225+1117)1717+4763)−3417+11atan⁡(426x(−11+17)17+11)−3411−17atan⁡(426x11−17(17+11))+114763−1717atan⁡(186826x4763−1717(1117+225))−192117+88121atan⁡(3442426x(3517+957)192117+88121))30056(2x4+11x2+13)\frac{4862 x \left(4 x^{2} + 11\right) - 442 x \left(22 x^{2} + 69\right) + \sqrt{442} \left(2 x^{4} + 11 x^{2} + 13\right) \left(- \sqrt{88121 - 1921 \sqrt{17}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(-957 + 35 \sqrt{17}\right) \sqrt{88121 - 1921 \sqrt{17}}} \right)} + 11 \sqrt{17 \sqrt{17} + 4763} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\left(-225 + 11 \sqrt{17}\right) \sqrt{17 \sqrt{17} + 4763}} \right)} - 34 \sqrt{\sqrt{17} + 11} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\left(-11 + \sqrt{17}\right) \sqrt{\sqrt{17} + 11}} \right)} - 34 \sqrt{11 - \sqrt{17}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{11 - \sqrt{17}} \left(\sqrt{17} + 11\right)} \right)} + 11 \sqrt{4763 - 17 \sqrt{17}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\sqrt{4763 - 17 \sqrt{17}} \left(11 \sqrt{17} + 225\right)} \right)} - \sqrt{1921 \sqrt{17} + 88121} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(35 \sqrt{17} + 957\right) \sqrt{1921 \sqrt{17} + 88121}} \right)}\right)}{30056 \left(2 x^{4} + 11 x^{2} + 13\right)}

  3. Añadimos la constante de integración:

    4862x(4x2+11)−442x(22x2+69)+442(2x4+11x2+13)(−88121−192117atan⁡(3442426x(−957+3517)88121−192117)+111717+4763atan⁡(186826x(−225+1117)1717+4763)−3417+11atan⁡(426x(−11+17)17+11)−3411−17atan⁡(426x11−17(17+11))+114763−1717atan⁡(186826x4763−1717(1117+225))−192117+88121atan⁡(3442426x(3517+957)192117+88121))30056(2x4+11x2+13)+constant\frac{4862 x \left(4 x^{2} + 11\right) - 442 x \left(22 x^{2} + 69\right) + \sqrt{442} \left(2 x^{4} + 11 x^{2} + 13\right) \left(- \sqrt{88121 - 1921 \sqrt{17}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(-957 + 35 \sqrt{17}\right) \sqrt{88121 - 1921 \sqrt{17}}} \right)} + 11 \sqrt{17 \sqrt{17} + 4763} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\left(-225 + 11 \sqrt{17}\right) \sqrt{17 \sqrt{17} + 4763}} \right)} - 34 \sqrt{\sqrt{17} + 11} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\left(-11 + \sqrt{17}\right) \sqrt{\sqrt{17} + 11}} \right)} - 34 \sqrt{11 - \sqrt{17}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{11 - \sqrt{17}} \left(\sqrt{17} + 11\right)} \right)} + 11 \sqrt{4763 - 17 \sqrt{17}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\sqrt{4763 - 17 \sqrt{17}} \left(11 \sqrt{17} + 225\right)} \right)} - \sqrt{1921 \sqrt{17} + 88121} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(35 \sqrt{17} + 957\right) \sqrt{1921 \sqrt{17} + 88121}} \right)}\right)}{30056 \left(2 x^{4} + 11 x^{2} + 13\right)}+ \mathrm{constant}

Respuesta:

4862x(4x2+11)−442x(22x2+69)+442(2x4+11x2+13)(−88121−192117atan⁡(3442426x(−957+3517)88121−192117)+111717+4763atan⁡(186826x(−225+1117)1717+4763)−3417+11atan⁡(426x(−11+17)17+11)−3411−17atan⁡(426x11−17(17+11))+114763−1717atan⁡(186826x4763−1717(1117+225))−192117+88121atan⁡(3442426x(3517+957)192117+88121))30056(2x4+11x2+13)+constant\frac{4862 x \left(4 x^{2} + 11\right) - 442 x \left(22 x^{2} + 69\right) + \sqrt{442} \left(2 x^{4} + 11 x^{2} + 13\right) \left(- \sqrt{88121 - 1921 \sqrt{17}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(-957 + 35 \sqrt{17}\right) \sqrt{88121 - 1921 \sqrt{17}}} \right)} + 11 \sqrt{17 \sqrt{17} + 4763} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\left(-225 + 11 \sqrt{17}\right) \sqrt{17 \sqrt{17} + 4763}} \right)} - 34 \sqrt{\sqrt{17} + 11} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\left(-11 + \sqrt{17}\right) \sqrt{\sqrt{17} + 11}} \right)} - 34 \sqrt{11 - \sqrt{17}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{11 - \sqrt{17}} \left(\sqrt{17} + 11\right)} \right)} + 11 \sqrt{4763 - 17 \sqrt{17}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{\sqrt{4763 - 17 \sqrt{17}} \left(11 \sqrt{17} + 225\right)} \right)} - \sqrt{1921 \sqrt{17} + 88121} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{\left(35 \sqrt{17} + 957\right) \sqrt{1921 \sqrt{17} + 88121}} \right)}\right)}{30056 \left(2 x^{4} + 11 x^{2} + 13\right)}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
 |                                    _______________                                                            _______________                                                                 ________________________                                                                                     ________________________                                                                                   __________________                                                                             __________________                                                                                                                             
 |           4                       /          ____      /                        ____                 \       /          ____      /                         ____                  \          /                   ____      /                                     ____                          \          /                   ____      /                                    ____                         \          /             ____      /                                ____                       \          /             ____      /                                 ____                        \           /    3       \               /   3       \    
 |          x                       /   11    \/ 17       |                  4*x*\/ 26                  |      /   11    \/ 17       |                   4*x*\/ 26                   |         /    88121     113*\/ 17       |                           34424*x*\/ 26                           |         /    88121     113*\/ 17       |                          34424*x*\/ 26                          |         /    4763    \/ 17       |                       1868*x*\/ 26                        |         /    4763    \/ 17       |                        1868*x*\/ 26                         |        13*\22*x  + 69*x/            11*\4*x  + 11*x/    
 | -------------------- dx = C -   /   ---- - ------ *atan|---------------------------------------------| -   /   ---- + ------ *atan|-----------------------------------------------| - 13*  /   --------- - ---------- *atan|-------------------------------------------------------------------| - 13*  /   --------- + ---------- *atan|-----------------------------------------------------------------| + 11*  /   ------- - ------ *atan|-----------------------------------------------------------| + 11*  /   ------- + ------ *atan|-------------------------------------------------------------| - --------------------------- + ------------------------
 |                    2          \/    1768    1768       |      _____________             _____________|   \/    1768    1768       |        _____________             _____________|      \/    345403552    20317856       |         _____________________                _____________________|      \/    345403552    20317856       |       _____________________                _____________________|      \/    2043808   120224      |       __________________                __________________|      \/    2043808   120224      |         __________________                __________________|     /            4         2\     /          4        2\
 | /   4       2     \                                    |     /        ____      ____   /        ____ |                            |       /        ____      ____   /        ____ |                                        |        /                ____         ____   /                ____ |                                        |      /                ____         ____   /                ____ |                                  |      /             ____         ____   /             ____ |                                  |        /             ____         ____   /             ____ |   2*\5746 + 884*x  + 4862*x /   2*\442 + 68*x  + 374*x /
 | \2*x  + 11*x  + 13/                                    \11*\/  11 - \/ 17   + \/ 17 *\/  11 - \/ 17  /                            \- 11*\/  11 + \/ 17   + \/ 17 *\/  11 + \/ 17  /                                        \- 957*\/  88121 - 1921*\/ 17   + 35*\/ 17 *\/  88121 - 1921*\/ 17  /                                        \957*\/  88121 + 1921*\/ 17   + 35*\/ 17 *\/  88121 + 1921*\/ 17  /                                  \225*\/  4763 - 17*\/ 17   + 11*\/ 17 *\/  4763 - 17*\/ 17  /                                  \- 225*\/  4763 + 17*\/ 17   + 11*\/ 17 *\/  4763 + 17*\/ 17  /                                                         
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
/
∫x4((2x4+11x2)+13)2 dx=C+11(4x3+11x)2(68x4+374x2+442)−13(22x3+69x)2(884x4+4862x2+5746)−111768−171768atan⁡(426x1711−17+1111−17)+1147632043808−17120224atan⁡(186826x11174763−1717+2254763−1717)−131131720317856+88121345403552atan⁡(3442426x3517192117+88121+957192117+88121)−1388121345403552−1131720317856atan⁡(3442426x−95788121−192117+351788121−192117)−171768+111768atan⁡(426x−1117+11+1717+11)+1117120224+47632043808atan⁡(186826x−2251717+4763+11171717+4763)\int \frac{x^{4}}{\left(\left(2 x^{4} + 11 x^{2}\right) + 13\right)^{2}}\, dx = C + \frac{11 \left(4 x^{3} + 11 x\right)}{2 \left(68 x^{4} + 374 x^{2} + 442\right)} - \frac{13 \left(22 x^{3} + 69 x\right)}{2 \left(884 x^{4} + 4862 x^{2} + 5746\right)} - \sqrt{\frac{11}{1768} - \frac{\sqrt{17}}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{\sqrt{17} \sqrt{11 - \sqrt{17}} + 11 \sqrt{11 - \sqrt{17}}} \right)} + 11 \sqrt{\frac{4763}{2043808} - \frac{\sqrt{17}}{120224}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{11 \sqrt{17} \sqrt{4763 - 17 \sqrt{17}} + 225 \sqrt{4763 - 17 \sqrt{17}}} \right)} - 13 \sqrt{\frac{113 \sqrt{17}}{20317856} + \frac{88121}{345403552}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{35 \sqrt{17} \sqrt{1921 \sqrt{17} + 88121} + 957 \sqrt{1921 \sqrt{17} + 88121}} \right)} - 13 \sqrt{\frac{88121}{345403552} - \frac{113 \sqrt{17}}{20317856}} \operatorname{atan}{\left(\frac{34424 \sqrt{26} x}{- 957 \sqrt{88121 - 1921 \sqrt{17}} + 35 \sqrt{17} \sqrt{88121 - 1921 \sqrt{17}}} \right)} - \sqrt{\frac{\sqrt{17}}{1768} + \frac{11}{1768}} \operatorname{atan}{\left(\frac{4 \sqrt{26} x}{- 11 \sqrt{\sqrt{17} + 11} + \sqrt{17} \sqrt{\sqrt{17} + 11}} \right)} + 11 \sqrt{\frac{\sqrt{17}}{120224} + \frac{4763}{2043808}} \operatorname{atan}{\left(\frac{1868 \sqrt{26} x}{- 225 \sqrt{17 \sqrt{17} + 4763} + 11 \sqrt{17} \sqrt{17 \sqrt{17} + 4763}} \right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.0000.002
Trazar el gráfico f(x)
Respuesta [src] 
             _________________                                                                          _________________                                                              
            /            ____                                                                          /            ____                                                               
 37        /   4763    \/ 17       /                           934                           \        /   4763    \/ 17       /                          934                          \
--- + 2*  /   ------ - ------ *atan|---------------------------------------------------------| + 2*  /   ------ + ------ *atan|-------------------------------------------------------|
884     \/    314432   18496       |        __________________             __________________|     \/    314432   18496       |      __________________             __________________|
                                   |       /             ____      ____   /             ____ |                                |     /             ____      ____   /             ____ |
                                   \- 22*\/  4763 - 17*\/ 17   + \/ 17 *\/  4763 - 17*\/ 17  /                                \22*\/  4763 + 17*\/ 17   + \/ 17 *\/  4763 + 17*\/ 17  /
24763314432−1718496atan⁡(934−224763−1717+174763−1717)+37884+21718496+4763314432atan⁡(934171717+4763+221717+4763)2 \sqrt{\frac{4763}{314432} - \frac{\sqrt{17}}{18496}} \operatorname{atan}{\left(\frac{934}{- 22 \sqrt{4763 - 17 \sqrt{17}} + \sqrt{17} \sqrt{4763 - 17 \sqrt{17}}} \right)} + \frac{37}{884} + 2 \sqrt{\frac{\sqrt{17}}{18496} + \frac{4763}{314432}} \operatorname{atan}{\left(\frac{934}{\sqrt{17} \sqrt{17 \sqrt{17} + 4763} + 22 \sqrt{17 \sqrt{17} + 4763}} \right)} 
=
= 
             _________________                                                                          _________________                                                              
            /            ____                                                                          /            ____                                                               
 37        /   4763    \/ 17       /                           934                           \        /   4763    \/ 17       /                          934                          \
--- + 2*  /   ------ - ------ *atan|---------------------------------------------------------| + 2*  /   ------ + ------ *atan|-------------------------------------------------------|
884     \/    314432   18496       |        __________________             __________________|     \/    314432   18496       |      __________________             __________________|
                                   |       /             ____      ____   /             ____ |                                |     /             ____      ____   /             ____ |
                                   \- 22*\/  4763 - 17*\/ 17   + \/ 17 *\/  4763 - 17*\/ 17  /                                \22*\/  4763 + 17*\/ 17   + \/ 17 *\/  4763 + 17*\/ 17  /
24763314432−1718496atan⁡(934−224763−1717+174763−1717)+37884+21718496+4763314432atan⁡(934171717+4763+221717+4763)2 \sqrt{\frac{4763}{314432} - \frac{\sqrt{17}}{18496}} \operatorname{atan}{\left(\frac{934}{- 22 \sqrt{4763 - 17 \sqrt{17}} + \sqrt{17} \sqrt{4763 - 17 \sqrt{17}}} \right)} + \frac{37}{884} + 2 \sqrt{\frac{\sqrt{17}}{18496} + \frac{4763}{314432}} \operatorname{atan}{\left(\frac{934}{\sqrt{17} \sqrt{17 \sqrt{17} + 4763} + 22 \sqrt{17 \sqrt{17} + 4763}} \right)} 
37/884 + 2*sqrt(4763/314432 - sqrt(17)/18496)*atan(934/(-22*sqrt(4763 - 17*sqrt(17)) + sqrt(17)*sqrt(4763 - 17*sqrt(17)))) + 2*sqrt(4763/314432 + sqrt(17)/18496)*atan(934/(22*sqrt(4763 + 17*sqrt(17)) + sqrt(17)*sqrt(4763 + 17*sqrt(17))))
Respuesta numérica [src] 
0.000440358559791355
0.000440358559791355

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

    © Sr Examen – Калькулятор