Numerical integration methods applicable to a type of definite integral

[Tachyonomad]

Numerical integration methods applicable to a type of definite integrl

Hey, so I've been working on a program to numerically integrate an integral of the form

∫xⁿf(x) dx, LIM(0 to INF.)

Here n can go to negative non integral values, say -3.7 etc. and f(x)
is a function of sin, cos and x's.
I want to know which numerical integration method I should be using for this
type of definite integral. I was looking at Gauss-Laguerre quadrature method, but I don't
know it it will be applicable, given the constraint on n to be > -1

(http://en.wikipedia.org/wiki/Gauss–Laguerre_quadrature#Generalized_Gauss.E2.80.93Laguerre_quadrature)

Also, there is a singularity at x=0, which will affect it.
Can anyone given any tips on how to handle this ?

 

[jasonRF]

Note that if the integral doesn't converge then no numerical algorithm will help you. If n=-3.7, then near zero your f needs to look like $f(x)\approx x^a$ for $a>2.7$ for the integral to exist. That is why generalized Gauss-Laguerre has the n>-1 condition. Conditions as $x\rightarrow \infty$ must also be met of course. The exponential in Gauss-Laguerre also helps with this.

jason