Sr Examen
Integral de 1/(x^3-2x)^2 dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | 2 | / 3 \ | \x - 2*x/ | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{3} - 2 x\right)^{2}}\, dx$$
Integral(1/((x^3 - 2*x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___\
| ___ |x*\/ 2 |
/ / / ___\ / ___\\ |-\/ 2 *acoth|-------|
| | | x*\/ 2 | | x*\/ 2 || | \ 2 / 2
| | log|-1 + -------| log|1 + -------|| |---------------------- for x > 2
| ___ | 1 1 \ 2 / \ 2 /| | 2
|\/ 2 *|- --------------- - ---------------- - ----------------- + ----------------| <
< | / ___\ / ___\ 4 4 | | / ___\
| | | x*\/ 2 | | x*\/ 2 | | | ___ |x*\/ 2 |
| | 4*|1 + -------| 4*|-1 + -------| | |-\/ 2 *atanh|-------|
/ | \ \ 2 / \ 2 / / / ___ ___\ | \ 2 / 2
| |----------------------------------------------------------------------------------- for And\x > -\/ 2 , x < \/ 2 / |---------------------- for x < 2
| 1 \ 4 1 \ 2
| ----------- dx = C + -------------------------------------------------------------------------------------------------------------------- - --- - -----------------------------------
| 2 2 4*x 4
| / 3 \
| \x - 2*x/
|
/
$$\int \frac{1}{\left(x^{3} - 2 x\right)^{2}}\, dx = C + \frac{\begin{cases} \frac{\sqrt{2} \left(- \frac{\log{\left(\frac{\sqrt{2} x}{2} - 1 \right)}}{4} + \frac{\log{\left(\frac{\sqrt{2} x}{2} + 1 \right)}}{4} - \frac{1}{4 \left(\frac{\sqrt{2} x}{2} + 1\right)} - \frac{1}{4 \left(\frac{\sqrt{2} x}{2} - 1\right)}\right)}{4} & \text{for}\: x > - \sqrt{2} \wedge x < \sqrt{2} \end{cases}}{2} - \frac{\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases}}{4} - \frac{1}{4 x}$$
Gráfica
Respuesta
[src]
___ / / ___\\
3*\/ 2 *\pi*I + log\-1 + \/ 2 //
oo - --------------------------------
32
$$\infty - \frac{3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{32}$$
=
=
___ / / ___\\
3*\/ 2 *\pi*I + log\-1 + \/ 2 //
oo - --------------------------------
32
$$\infty - \frac{3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{32}$$
oo - 3*sqrt(2)*(pi*i + log(-1 + sqrt(2)))/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.