I am brain dead at this point and I'm not sure how to do this integral. Any help would be appreciated.

$\displaystyle E(X)= (12/5)\intop_{0}^{\infty}x(1+\frac{x}{2.5})^{-7}dx$

The original was easy$\displaystyle k\intop_{0}^{\infty}(1+\frac{x}{2.5})^{-7}dx=\frac{-5k}{12}(1+\frac{x}{2.5})^{-6}\mid_{0}^{\infty}=\frac{5k}{12} $ This integral must equal 1 so k=12/5.

Integrate by parts? Partial fractions? I just can't think how to approach this expected value problem.