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