Sr Examen
Integral de x^2/(5-x^6) dx
Solución
Ha introducido
[src]
1 / | | 2 | x | ------ dx | 6 | 5 - x | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{5 - x^{6}}\, dx$$
Integral(x^2/(5 - x^6), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ 3\ \
|| ___ |\/ 5 *x | |
/ ||-\/ 5 *acoth|--------| |
| || \ 5 / 6 |
| 2 ||----------------------- for x > 5|
| x || 15 |
| ------ dx = C - |< |
| 6 || / ___ 3\ |
| 5 - x || ___ |\/ 5 *x | |
| ||-\/ 5 *atanh|--------| |
/ || \ 5 / 6 |
||----------------------- for x < 5|
\\ 15 /
$$\int \frac{x^{2}}{5 - x^{6}}\, dx = C - \begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} x^{3}}{5} \right)}}{15} & \text{for}\: x^{6} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} x^{3}}{5} \right)}}{15} & \text{for}\: x^{6} < 5 \end{cases}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\-1 + \/ 5 // \/ 5 *log\\/ 5 / \/ 5 *\pi*I + log\\/ 5 // \/ 5 *log\1 + \/ 5 /
- ------------------------------ - ---------------- + ------------------------- + --------------------
30 30 30 30
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{30} + \frac{\sqrt{5} \log{\left(1 + \sqrt{5} \right)}}{30} - \frac{\sqrt{5} \left(\log{\left(-1 + \sqrt{5} \right)} + i \pi\right)}{30} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{30}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 5 *\pi*I + log\-1 + \/ 5 // \/ 5 *log\\/ 5 / \/ 5 *\pi*I + log\\/ 5 // \/ 5 *log\1 + \/ 5 /
- ------------------------------ - ---------------- + ------------------------- + --------------------
30 30 30 30
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{30} + \frac{\sqrt{5} \log{\left(1 + \sqrt{5} \right)}}{30} - \frac{\sqrt{5} \left(\log{\left(-1 + \sqrt{5} \right)} + i \pi\right)}{30} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{30}$$
-sqrt(5)*(pi*i + log(-1 + sqrt(5)))/30 - sqrt(5)*log(sqrt(5))/30 + sqrt(5)*(pi*i + log(sqrt(5)))/30 + sqrt(5)*log(1 + sqrt(5))/30
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.