Mister Exam

Other calculators

Solving integrals/ exp(-x)*ln((x-1)/(x+1))

Integral of exp(-x)*ln((x-1)/(x+1)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [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))
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/
 |                            |                                               
/                            /
$$\int e^{- x} \log{\left(\frac{x - 1}{x + 1} \right)}\, dx = C + 2 \int \frac{e^{- x}}{\left(x - 1\right) \left(x + 1\right)}\, dx - e^{- x} \log{\left(\frac{x}{x + 1} - \frac{1}{x + 1} \right)}$$
Simplify
The answer [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)

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator