Sr Examen
Integral de ln(x-1)/x dx
Solución
Ha introducido
[src]
1 / | | log(x - 1) | ---------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x - 1 \right)}}{x}\, dx$$
Integral(log(x - 1)/x, (x, 0, 1))
Respuesta (Indefinida)
[src]
// -polylog(2, x) + pi*I*log(x) for |x| < 1\
/ || |
| || /1\ 1 |
| log(x - 1) || -polylog(2, x) - pi*I*log|-| for --- < 1|
| ---------- dx = C + |< \x/ |x| |
| x || |
| || __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 | / /
$$\int \frac{\log{\left(x - 1 \right)}}{x}\, dx = C + \begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{otherwise} \end{cases}$$
Respuesta
[src]
2
pi
oo*I - ---
6
$$- \frac{\pi^{2}}{6} + \infty i$$
=
=
2
pi
oo*I - ---
6
$$- \frac{\pi^{2}}{6} + \infty i$$
oo*i - pi^2/6
Respuesta numérica
[src]
(-1.64493406684823 + 138.514221668049j)
(-1.64493406684823 + 138.514221668049j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.