Numerical Integration in 1D

On Fri, 7 Mar 2008, Max wrote:

Dear UseRs,

I'm curious about the derivative of n!.

We know that Gamma(n+1)=n! So when on takes the derivative of
Gamma(n+1) we get Int(ln(x)*exp(-x)*x^n,x=0..Inf).

I've tried code like

integrand<-function(x) {log(x)*exp(x)*x^n}
integrate(integrand,lower=0,upper=Inf)

It seems that R doesn't like to integrate for any n, and I was
wondering if anyone knew a way around this?

ln(x) e^x x^n is not integrable on (0, Inf).  You presumably slipped over 
a minus sign, but your definition of gamma(n) is wrong -- see ?gamma.

integrate(function(x) exp(-x)*x^n, lower=0, upper=Inf)

will work for gamma(n+1).

integrand<-function(x) {log(x)*exp(-x)*x^n}
integrate(integrand,lower=0,upper=Inf)