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Resolución de integrales/ (x^3)/ (x^3)/(x^8-2)

Integral de (x^3)/(x^8-2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |     3     
 |    x      
 |  ------ dx
 |   8       
 |  x  - 2   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x^{3}}{x^{8} - 2}\, dx$$ 
Integral(x^3/(x^8 - 2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                   //            /  ___  4\             \
                   ||   ___      |\/ 2 *x |             |
  /                ||-\/ 2 *acoth|--------|             |
 |                 ||            \   2    /        8    |
 |    3            ||-----------------------  for x  > 2|
 |   x             ||           8                       |
 | ------ dx = C + |<                                   |
 |  8              ||            /  ___  4\             |
 | x  - 2          ||   ___      |\/ 2 *x |             |
 |                 ||-\/ 2 *atanh|--------|             |
/                  ||            \   2    /        8    |
                   ||-----------------------  for x  < 2|
                   \\           8                       /
$$\int \frac{x^{3}}{x^{8} - 2}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{8} & \text{for}\: x^{8} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{8} & \text{for}\: x^{8} < 2 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\
  \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /
- ------------------------- - -------------------- + ------------------------------ + ----------------
              16                       16                          16                        16
$$- \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{16} + \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{16} - \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{16} + \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{16}$$ 
=
= 
    ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\
  \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /
- ------------------------- - -------------------- + ------------------------------ + ----------------
              16                       16                          16                        16
$$- \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{16} + \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{16} - \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{16} + \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{16}$$ 
-sqrt(2)*(pi*i + log(sqrt(2)))/16 - sqrt(2)*log(1 + sqrt(2))/16 + sqrt(2)*(pi*i + log(-1 + sqrt(2)))/16 + sqrt(2)*log(sqrt(2))/16
Respuesta numérica [src] 
-0.155806310035058
-0.155806310035058

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

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