# Double integral variable separation

1. Jul 2, 2009

### rman144

$$\int$$$$^{B}______________{A}$$$$\int$$$$^{\infty}_______________{0}$$$$\frac{t^{N-1}x^{s-N-1}dtdx}{e^{t+x}+1}$$

With the restrictions that that B>A, 0<Re(s)<1 and N is a natural number>1.

I think t=ab and x=a(1-b) would work, but I'm not sure how to go from there. I don't need to solve the integral; just rewrite it in terms of two separate integrals, each of a single variable.

Also, that dx should be on the right of the fraction bar; I cannot seem to locate the correct formatting to make this happen.

Finally, what is the solution when A=0 and B=oo?

2. Jul 3, 2009

### daviddoria

You just have to put the dx after the 'frac', if I understood your latex question:
$$\frac{t^{N-1}x^{s-N-1}dt}{e^{t+x}+1}dx$$