# Find upper limit of improper integral - Numerical Integration

1. Feb 26, 2012

### architect

Find upper limit of improper integral -- Numerical Integration

Hi,

I have the following complicated integral willing to integrate numerically. The integral is:

$\int _0^{\infty }x\frac{\beta^\alpha}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\beta/x}dx$.

We know that the integral converges to:
$((1/\beta)^\alpha \beta^{\alpha+1})/(\alpha-1)$.

Can anyone suggest a methodology of deriving the upper bound of the limit of this integral for numerical evaluation purposes?