# An integration step in PDE by Laplace transform method

• Oct 22nd 2011, 08:34 AM
math2011
An integration step in PDE by Laplace transform method
I am stuck with an integration step in solving a PDE by Laplace transform.

The integration is $\int e^{\frac{s x^2}{2}} \frac{x}{s} dx = \frac{1}{s^2} e^{\frac{s x^2}{2}}$. How is the integral obtained? I want to use integration by parts but I don't know how to integrate $e^{\frac{sx^2}{2}}$.
• Oct 22nd 2011, 08:50 AM
Jester
Re: An integration step in PDE by Laplace transform method
Let $u = \frac{sx^2}{2}$. The integration will come out fine!
• Oct 22nd 2011, 04:23 PM
math2011
Re: An integration step in PDE by Laplace transform method
Thank you. That worked.