Integration Evaluation

1. Apr 13, 2010

S_David

Hello,

I am reading some material that using mathematics extensively, and I encountered with the following result:

$$\frac{N}{\overline{\gamma}}\,\int_0^{\infty}\gamma \,\left[1-\mbox{e}^{-\gamma/\overline{\gamma}}\right]^{N-1}\,\mbox{e}^{-\gamma/\overline{\gamma}}\,d\gamma=\,\overline{\gamma}\sum_{k=1}^N\frac{1}{k}$$

How did they get there? I tried to use the binomial expansion and assemble the exponentials, but the result was something different. Any hint will be highly appreciated.