I can also suggest you the use of "maxima" http://maxima.sourceforge.net/
It is a very powerful symbolic math tool under GNU license. Using it I obtained the following answer to you question:
-π/(4•√a) if a≧ 0
j•π•√-a/(4•a) if a<0 (j is the complex operator)
also you can perfom the indefinite integration and see the primitive of your function.