Momentum Space

I need some help in finishing this problem. I normalized the wavefunction and C to be equal to sqrt(a/2). I think this is the correct answer unless I made some mistake when integrating. Also, I do now know how to do the second part of the problem when it asks you to find a(p). Particularly, I am having problems with the integral. I looked up some integral tables but did not find anything useful. There is probably some trick to doing this integral that I'm not seeing.