Sr Examen
Integral de lnt/(t-3) dx
Solución
Ha introducido
[src]
1 / | | log(t) | ------ dt | t - 3 | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(t \right)}}{t - 3}\, dt$$
Integral(log(t)/(t - 3), (t, 0, 1))
Respuesta (Indefinida)
[src]
// / pi*I\ \
|| | (-3 + t)*e | |
|| - polylog|2, --------------| + log(3)*log(-3 + t) for |-3 + t| < 1|
|| \ 3 / |
/ || |
| || / pi*I\ |
| log(t) || | (-3 + t)*e | / 1 \ 1 |
| ------ dt = C + |< - polylog|2, --------------| - log(3)*log|------| for -------- < 1|
| t - 3 || \ 3 / \-3 + t/ |-3 + t| |
| || |
/ || / pi*I\ |
|| | (-3 + t)*e | __0, 2 /1, 1 | \ __2, 0 / 1, 1 | \ |
||- polylog|2, --------------| + log(3)*/__ | | -3 + t| - log(3)*/__ | | -3 + t| otherwise |
|| \ 3 / \_|2, 2 \ 0, 0 | / \_|2, 2 \0, 0 | / |
\\ /
$$\int \frac{\log{\left(t \right)}}{t - 3}\, dt = C + \begin{cases} \log{\left(3 \right)} \log{\left(t - 3 \right)} - \operatorname{Li}_{2}\left(\frac{\left(t - 3\right) e^{i \pi}}{3}\right) & \text{for}\: \left|{t - 3}\right| < 1 \\- \log{\left(3 \right)} \log{\left(\frac{1}{t - 3} \right)} - \operatorname{Li}_{2}\left(\frac{\left(t - 3\right) e^{i \pi}}{3}\right) & \text{for}\: \frac{1}{\left|{t - 3}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {t - 3} \right)} \log{\left(3 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {t - 3} \right)} \log{\left(3 \right)} - \operatorname{Li}_{2}\left(\frac{\left(t - 3\right) e^{i \pi}}{3}\right) & \text{otherwise} \end{cases}$$
Respuesta
[src]
2
pi
-polylog(2, 2/3) + --- + (pi*I + log(2))*log(3) - (pi*I + log(3))*log(3)
6
$$- \operatorname{Li}_{2}\left(\frac{2}{3}\right) + \frac{\pi^{2}}{6} - \left(\log{\left(3 \right)} + i \pi\right) \log{\left(3 \right)} + \left(\log{\left(2 \right)} + i \pi\right) \log{\left(3 \right)}$$
=
=
2
pi
-polylog(2, 2/3) + --- + (pi*I + log(2))*log(3) - (pi*I + log(3))*log(3)
6
$$- \operatorname{Li}_{2}\left(\frac{2}{3}\right) + \frac{\pi^{2}}{6} - \left(\log{\left(3 \right)} + i \pi\right) \log{\left(3 \right)} + \left(\log{\left(2 \right)} + i \pi\right) \log{\left(3 \right)}$$
-polylog(2, 2/3) + pi^2/6 + (pi*i + log(2))*log(3) - (pi*i + log(3))*log(3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.