(1)
y ' = xcosx
y = ∫ xcosxdx
= ∫ xdsinx
= xsinx - ∫ sinxdx
= xsinx + cosx + C ( C is a constant )
(2)
y' = xe^x
y = ∫ xe^x dx
= ∫ xde^x
= xe^x - ∫ e^xdx
= xe^x - e^x + C