
Re: Removing singularity at x=0 for integral
Posted:
Nov 26, 2013 3:10 PM


On 26.11.2013 16:10, dspguy2@netscape.net wrote: > Hi I'm trying to numerically integrate the following expression from 0 .. 1 > f(x)=1/x^1.5 * exp(A/x) , where A is a constant. > > As x>0, the exponential goes to zero faster than the power, so f(x)>0, as x> 0. > I'm evaluating this integral at various values of A  there are cases when A is very small. > > I'm trying to find a way to remove the singularity at x=0. I've looked at the usual techniques, like integration by parts, subtracting the singularity out, change of variables. > > The change of variables is usually done when the power is less than one e.g.(1/sqrt(x)). exp(A/x) is not analytic so integration by parts seems problematic. > > Any suggestions? > > Thanks for any assistance. > David
Guessing you mean 0 < A the value is Pi^(1/2)*(erf(A^(1/2))1)/A^(1/2) by Maple
Note that you do not need 'analytic', so x = 1/t^2 is allowed here and will give what Maple says for Int(2*exp(A*t^2), t = 1 .. infinity)

