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 $\displaystyle \int e^{\frac{s x^2}{2}} \frac{x}{s} dx = \frac{1}{s^2} e^{\frac{s x^2}{2}}$. How is the integral obtained? I want to use integration by parts but I don't know how to integrate $\displaystyle e^{\frac{sx^2}{2}}$.

Re: An integration step in PDE by Laplace transform method

Let $\displaystyle u = \frac{sx^2}{2}$. The integration will come out fine!

Re: An integration step in PDE by Laplace transform method