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