Sr Examen
Integral de exp(-x)*ln((x-1)/(x+1)) dx
Solución
Ha introducido
[src]
oo / | | -x /x - 1\ | e *log|-----| dx | \x + 1/ | / 1
$$\int\limits_{1}^{\infty} e^{- x} \log{\left(\frac{x - 1}{x + 1} \right)}\, dx$$
Integral(exp(-x)*log((x - 1)/(x + 1)), (x, 1, oo))
Respuesta
[src]
/ / pi*I\ / pi*I\\ -1 / / pi*I\ / pi*I\\ -1 -1 __1, 3 /0, 1, 1 | \ -2 / -1\ -1
\- Ei\e / + pi*I + log\-e //*e - \- Ei\e / + pi*I + EulerGamma + log\-e //*e - e */__ | | 1/2| - e *log(2) - \1 - e /*e *log(2)
\_|3, 2 \ 1 0 | /
$$- \frac{\left(1 - e^{-1}\right) \log{\left(2 \right)}}{e} - \frac{{G_{3, 2}^{1, 3}\left(\begin{matrix} 0, 1, 1 & \\1 & 0 \end{matrix} \middle| {\frac{1}{2}} \right)}}{e} - \frac{\log{\left(2 \right)}}{e^{2}} + \frac{\log{\left(- e^{i \pi} \right)} - \operatorname{Ei}{\left(e^{i \pi} \right)} + i \pi}{e} - \frac{\log{\left(- e^{i \pi} \right)} + \gamma - \operatorname{Ei}{\left(e^{i \pi} \right)} + i \pi}{e}$$
=
=
/ / pi*I\ / pi*I\\ -1 / / pi*I\ / pi*I\\ -1 -1 __1, 3 /0, 1, 1 | \ -2 / -1\ -1
\- Ei\e / + pi*I + log\-e //*e - \- Ei\e / + pi*I + EulerGamma + log\-e //*e - e */__ | | 1/2| - e *log(2) - \1 - e /*e *log(2)
\_|3, 2 \ 1 0 | /
$$- \frac{\left(1 - e^{-1}\right) \log{\left(2 \right)}}{e} - \frac{{G_{3, 2}^{1, 3}\left(\begin{matrix} 0, 1, 1 & \\1 & 0 \end{matrix} \middle| {\frac{1}{2}} \right)}}{e} - \frac{\log{\left(2 \right)}}{e^{2}} + \frac{\log{\left(- e^{i \pi} \right)} - \operatorname{Ei}{\left(e^{i \pi} \right)} + i \pi}{e} - \frac{\log{\left(- e^{i \pi} \right)} + \gamma - \operatorname{Ei}{\left(e^{i \pi} \right)} + i \pi}{e}$$
(-Ei(exp_polar(pi*i)) + pi*i + log(-exp_polar(pi*i)))*exp(-1) - (-Ei(exp_polar(pi*i)) + pi*i + EulerGamma + log(-exp_polar(pi*i)))*exp(-1) - exp(-1)*meijerg(((0, 1, 1), ()), ((1,), (0,)), 1/2) - exp(-2)*log(2) - (1 - exp(-1))*exp(-1)*log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.