How to integrate -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt

[lamba89]

Hi, I'm currently studying for my PDE exam, but my fundamental calculus skills might not be the best.

I typed my question into wolfram alpha (http://www.wolframalpha.com/input/?i=integrate+-exp((s^2+-+t^2)/2)*(f'(t)+-+t*f(t))+dt) and the result is correct, but I don't know how it got there. Can someone please explain to me?

Thanks!

 

[appelberry]

Apply the product rule for differentiation to the solution. This gives you the integrand. If you recognize this then you just need to do the reverse to get the solution.

 

[lamba89]

Thanks, I just realized it too