(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to solve:

[tex]\int_{-\infty}^{\infty}xe^{(a-x)^2}dx[/tex]

2. Relevant equations

3. The attempt at a solution

My first intuition would be to rewrite this as:

[tex]\oint_cze^{(a-z)^2}dz[/tex]

and then use Cauchy's Residue theorem to calculate the integral. There is one singularity at [itex]x_o=0[/itex] when [itex]x[/itex]->[itex]\infty[/itex]. To calculate the residue,

[tex]Res(z_o)=(z-z_o)f(z) |_{z=z_o}[/tex]

where in this case

[tex]f(z)=ze^{(a-x)^2}[/tex]

So, we have

[tex]Res(0)=(z-0)ze^{(a-z)^2}|_{z=0}[/tex]

[tex]=0[/tex]

which is clearly not right (mathematica gives [itex]a\sqrt{\pi}[/itex]. What am I doing wrong? Any hints? Thanks!

EDIT: if you take the derivative of the residue twice and then taking the limit you get [itex]2e^{-a^2}[/itex], and multiplying this by [itex]2\pi i[/itex] still doesn't give the answer!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex integral

**Physics Forums | Science Articles, Homework Help, Discussion**