- #1
msenay
- 5
- 0
Homework Statement
I need to solve this integral,
$$\int _{-\infty }^{\infty }x\left( \dfrac {1} {1-e^{-x}}+\dfrac {1} {1+qe^{-x}}\right) dx$$
My advisor said its solution will be zero. But i haven't improved it yet. There is important case. This integral is divergent at x=0. So, i should separate two parts to teh integral. First part should be from -infinty to zero and second one should be from zero to infinty.
Homework Equations
I solved this integral $$\int _{-\infty }^{\infty }x^{2}\left( \dfrac {1} {1-e^{-x}}+\dfrac {1} {1+qe^{-x}}\right) dx=\sum _{n=1}^{\infty }\dfrac {1} {n^{3}}-\sum _{n=1}^{\infty }\dfrac {\left( -q^{-1}\right) ^{n}} {n^{3}}$$ This integral is even function (0 < q < 1). So, i can change the integral from zero to infinty instead of from -infinty to infinty.
The Attempt at a Solution
How can i solve this integral? Do you have any idea ?