# Challenging integral with exponential functions

1. Jul 22, 2009

### Devon79

1. The problem statement, all variables and given/known data

I'm unable to integrate the following function with respect to x [-inf, +inf]:

2. Relevant equations

exp(y*x)*(1+exp(x))^(-n)dx

3. The attempt at a solution

I tried to expand the function by distributing the exponent (-n) across the rightmost product, but I don't think its possible. Does a clever substitution method exist?

Last edited: Jul 22, 2009
2. Jul 22, 2009

### Count Iblis

Indefinite integral?

3. Jul 22, 2009

### Office_Shredder

Staff Emeritus
You can try some sort of induction argument. Integration by parts: eyx and dx/(1+ex)n probably gives you something based on the integral of $$\frac{e^{yx}}{(1+e^x)^{n-1}}$$