Sr Examen
Integral de (x^3)/(x^8-2) dx
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 /
$$\int \frac{x^{3}}{x^{8} - 2}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{8} & \text{for}\: x^{8} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{8} & \text{for}\: x^{8} < 2 \end{cases}$$
Gráfica
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
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.