Integral of exp(-x)*ln((x-1)/(x+1)) dx
The solution
The answer (Indefinite)
[src]
/
/ |
| | -x
| -x /x - 1\ | e -x / 1 x \
| e *log|-----| dx = C + 2* | ---------------- dx - e *log|- ----- + -----|
| \x + 1/ | (1 + x)*(-1 + x) \ 1 + x 1 + x/
| |
/ /
∫e−xlog(x+1x−1)dx=C+2∫(x−1)(x+1)e−xdx−e−xlog(x+1x−x+11)
/ / 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 | /
−e(1−e−1)log(2)−eG3,21,3(0,1,11021)−e2log(2)+elog(−eiπ)−Ei(eiπ)+iπ−elog(−eiπ)+γ−Ei(eiπ)+iπ
=
/ / 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 | /
−e(1−e−1)log(2)−eG3,21,3(0,1,11021)−e2log(2)+elog(−eiπ)−Ei(eiπ)+iπ−elog(−eiπ)+γ−Ei(eiπ)+iπ
(-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)
Use the examples entering the upper and lower limits of integration.