Challenging integral with exponential functions

[Devon79]

Homework Statement

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

Homework Equations

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

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?

 

[Count Iblis]

Indefinite integral?

 

[Office_Shredder]

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