Sr Examen
Integral de log(x+1)/(x+2) dx
Solución
Ha introducido
[src]
1 / | | log(x + 1) | ---------- dx | x + 2 | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x + 1 \right)}}{x + 2}\, dx$$
Integral(log(x + 1)/(x + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// -polylog(2, 2 + x) + pi*I*log(2 + x) for |2 + x| < 1\
/ || |
| || / 1 \ 1 |
| log(x + 1) || -polylog(2, 2 + x) - pi*I*log|-----| for ------- < 1|
| ---------- dx = C + |< \2 + x/ |2 + x| |
| x + 2 || |
| || __0, 2 /1, 1 | \ __2, 0 / 1, 1 | \ |
/ ||-polylog(2, 2 + x) + pi*I*/__ | | 2 + x| - pi*I*/__ | | 2 + x| otherwise |
\\ \_|2, 2 \ 0, 0 | / \_|2, 2 \0, 0 | / /
$$\int \frac{\log{\left(x + 1 \right)}}{x + 2}\, dx = C + \begin{cases} i \pi \log{\left(x + 2 \right)} - \operatorname{Li}_{2}\left(x + 2\right) & \text{for}\: \left|{x + 2}\right| < 1 \\- i \pi \log{\left(\frac{1}{x + 2} \right)} - \operatorname{Li}_{2}\left(x + 2\right) & \text{for}\: \frac{1}{\left|{x + 2}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x + 2} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x + 2} \right)} - \operatorname{Li}_{2}\left(x + 2\right) & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
2
pi
-polylog(2, 3) + --- + pi*I*log(3) - 2*pi*I*log(2)
4
$$\frac{\pi^{2}}{4} - 2 i \pi \log{\left(2 \right)} - \operatorname{Li}_{2}\left(3\right) + i \pi \log{\left(3 \right)}$$
=
=
2
pi
-polylog(2, 3) + --- + pi*I*log(3) - 2*pi*I*log(2)
4
$$\frac{\pi^{2}}{4} - 2 i \pi \log{\left(2 \right)} - \operatorname{Li}_{2}\left(3\right) + i \pi \log{\left(3 \right)}$$
-polylog(2, 3) + pi^2/4 + pi*i*log(3) - 2*pi*i*log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.