Sr Examen
Integral de 1/(x^3-2*x^2-x) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | 3 2 | x - 2*x - x | / 0
$$\int\limits_{0}^{1} \frac{1}{- x + \left(x^{3} - 2 x^{2}\right)}\, dx$$
Integral(1/(x^3 - 2*x^2 - x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 2 *(-1 + x)| |
||-\/ 2 *acoth|--------------| |
/ || \ 2 / 2 |
| / 2 \ ||----------------------------- for (-1 + x) > 2|
| 1 log\-1 + x - 2*x/ || 2 |
| ------------- dx = C + ------------------ - |< | - log(x)
| 3 2 2 || / ___ \ |
| x - 2*x - x || ___ |\/ 2 *(-1 + x)| |
| ||-\/ 2 *atanh|--------------| |
/ || \ 2 / 2 |
||----------------------------- for (-1 + x) < 2|
\\ 2 /
$$\int \frac{1}{- x + \left(x^{3} - 2 x^{2}\right)}\, dx = C - \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} < 2 \end{cases} - \log{\left(x \right)} + \frac{\log{\left(x^{2} - 2 x - 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ / 2 \\
| | / ___\ ||
| | |1 \/ 2 | ||
/ ___\ | | 56*|- - -----| ___||
|1 \/ 2 | | |21 \2 4 / 3*\/ 2 ||
-oo + |- - -----|*|pi*I + log|-- - --------------- + -------||
\2 4 / \ \17 17 17 //
$$-\infty + \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right) \left(\log{\left(- \frac{56 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{2}}{17} + \frac{3 \sqrt{2}}{17} + \frac{21}{17} \right)} + i \pi\right)$$
=
=
/ / 2 \\
| | / ___\ ||
| | |1 \/ 2 | ||
/ ___\ | | 56*|- - -----| ___||
|1 \/ 2 | | |21 \2 4 / 3*\/ 2 ||
-oo + |- - -----|*|pi*I + log|-- - --------------- + -------||
\2 4 / \ \17 17 17 //
$$-\infty + \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right) \left(\log{\left(- \frac{56 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{2}}{17} + \frac{3 \sqrt{2}}{17} + \frac{21}{17} \right)} + i \pi\right)$$
-oo + (1/2 - sqrt(2)/4)*(pi*i + log(21/17 - 56*(1/2 - sqrt(2)/4)^2/17 + 3*sqrt(2)/17))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.