# Divergent Integral and Mathematica

1. Jul 3, 2008

### gn0m0n

Hi,

I am trying to calculate a double integral, in Mathematica it could be denoted

Integrate[(x*y)/(x*y-m2/s2),{x,0,1},{y,0,1-x}]

That is,

$$\int$$$$\int$$$$\frac{xy}{(xy-m^{2}/s^{2})}$$dydx with boundaries y=0,y=1-x and x=0,x=1. m and s are constants, of course.

Now, I get some fairly crazy-looking and unhelpful results for the y-integral from Mathematica but I simply used a table of integrals and plugging in obtained

1-x+$$\frac{1}{x}$$*$$\frac{m^{2}}{s^{2}}$$*Ln|x-x^{2}-$$\frac{m^{2}}{s^{2}}$$|

Now of course when I integrate this from x=0 to x=1 then I have a problem as x goes to 0. Someone suggested using interpolation somehow but I know very little about that and don't see if this is where to apply it. I don't think the integral should be infinite - perhaps the y-integral was wrong?

Any help would be much appreciated!

2. Jul 3, 2008

### gn0m0n

I should have had a denominator of m^2/s^2 in the log there, or subtracted a log|^2/s^2|.

Anyway, that is not the problem...

Last edited: Jul 3, 2008