Well if you need a value, most/all scientific calculators will do definite integration. If you need the symbolics you're in the deep end.

This post was edited by Dontrunaway on Nov 12 2014 11:34pm

So first of all, not Castigliano's

secondly, I doubt you have to find the definite integral if there is any complex loadings
It's expected for you to break up the moments , calculate their areas and centroids
use centroids to find height at virtual moment
virtual load * deflection = sum (Area *h)/(Ei)

yea thats what im doin right now, my prof called it visual integration.

what if the moment is a cubic, and i gotta locate the centroid and area of it

or should I just break it up, and solve it using the cantilever method