Sr Examen
Integral de (1+ln(x-1))/x-1 dx
Solución
Ha introducido
[src]
2 e / | | /1 + log(x - 1) \ | |-------------- - 1| dx | \ x / | / 1 + E
$$\int\limits_{1 + e}^{e^{2}} \left(-1 + \frac{\log{\left(x - 1 \right)} + 1}{x}\right)\, dx$$
Integral((1 + log(x - 1))/x - 1, (x, 1 + E, exp(2)))
Respuesta (Indefinida)
[src]
// -polylog(2, x) + pi*I*log(x) for |x| < 1\
/ || |
| || /1\ 1 |
| /1 + log(x - 1) \ || -polylog(2, x) - pi*I*log|-| for --- < 1|
| |-------------- - 1| dx = C - x + |< \x/ |x| | + log(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 | / /
$$\int \left(-1 + \frac{\log{\left(x - 1 \right)} + 1}{x}\right)\, dx = C - x + \begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{otherwise} \end{cases} + \log{\left(x \right)}$$
Gráfica
Respuesta
[src]
2 / 2\ 3 + E - e - log(1 + E) - polylog\2, e / + 2*pi*I - pi*I*log(1 + E) + polylog(2, 1 + E)
$$- e^{2} - \log{\left(1 + e \right)} + e + 3 - i \pi \log{\left(1 + e \right)} + \operatorname{Li}_{2}\left(1 + e\right) - \operatorname{Li}_{2}\left(e^{2}\right) + 2 i \pi$$
=
=
2 / 2\ 3 + E - e - log(1 + E) - polylog\2, e / + 2*pi*I - pi*I*log(1 + E) + polylog(2, 1 + E)
$$- e^{2} - \log{\left(1 + e \right)} + e + 3 - i \pi \log{\left(1 + e \right)} + \operatorname{Li}_{2}\left(1 + e\right) - \operatorname{Li}_{2}\left(e^{2}\right) + 2 i \pi$$
3 + E - exp(2) - log(1 + E) - polylog(2, exp(2)) + 2*pi*i - pi*i*log(1 + E) + polylog(2, 1 + E)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.