An integration step in PDE by Laplace transform method

**math2011** · October 22nd 2011, 07:34 AM

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 $e^{\frac{sx^2}{2}}$ .

**Danny** · October 22nd 2011, 07:50 AM

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

**math2011** · October 22nd 2011, 03:23 PM

Thank you. That worked.

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