Sr Examen
Integral de ((x+1)ln(x))/(x-1) dx
Solución
Ha introducido
[src]
0 / | | (x + 1)*log(x) | -------------- dx | x - 1 | / 0
$$\int\limits_{0}^{0} \frac{\left(x + 1\right) \log{\left(x \right)}}{x - 1}\, dx$$
Integral(((x + 1)*log(x))/(x - 1), (x, 0, 0))
Respuesta (Indefinida)
[src]
// -polylog(2, x) + pi*I*log(x) for |x| < 1\
/ || |
| || /1\ 1 |
| (x + 1)*log(x) || -polylog(2, x) - pi*I*log|-| for --- < 1| / pi*I\
| -------------- dx = C - x - |< \x/ |x| | - polylog\2, (-1 + x)*e / + (x + log(-1 + x))*log(x)
| x - 1 || |
| || __0, 2 /1, 1 | \ __2, 0 / 1, 1 | \ |
/ ||-polylog(2, x) + pi*I*/__ | | x| - pi*I*/__ | | x| otherwise |
\\ \_|2, 2 \ 0, 0 | / \_|2, 2 \0, 0 | / /
$$\int \frac{\left(x + 1\right) \log{\left(x \right)}}{x - 1}\, dx = C - x + \left(x + \log{\left(x - 1 \right)}\right) \log{\left(x \right)} - \begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{otherwise} \end{cases} - \operatorname{Li}_{2}\left(\left(x - 1\right) e^{i \pi}\right)$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.