Monte-Carlo integration good ?

[Toan T Nguyen <toan.nguyen@physics.gatech.edu>]

Hello all,

I'm seeking advice as on how reliable the result of my numerical
integration is. I've been using the GSL Monte-Carlo integration
routines to perform a 3D integration of a function with
singularity at the origin. The integrand contains something similar to

exp( - k x) / x

The integration range is for 0 < x < 1. (However, since k ~ 50, only the 
range
0< x < 0.02 contributes most to the integration.)

Both GSL VEGAS and MISER algorithm gives more or less the same result.
But I'm a tiny bit suspect of the number that GSL gives.

My question is how reliable is this result. Are VEGAS/MISER algorithms
able to automatically focus on the 0<x<0.02 range instead of the full
integration range 0 < x < 1? Do I need to manually adjust the parameters
of the integration subroutine to handle this situation ? So far, I simply
follow the Monte-Carlo integration example to do the integration.

Thanks

Toan