Substitution method with Integration by Parts??? 1. The problem statement, all variables and given/known data Evaluate the integral... ∫x^3[e^(-x^2)]dx 2. Relevant equations ∫udv=uv-∫vdu 3. The attempt at a solution I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make it more complicated so I decided to use the substitution method setting y=-x^2 and dy=-2xdx and finally -1/2dy=xdx to give me 1/2∫ye^ydy From here i used integration by parts with u=y, du=dy, v=e^y and dv=e^y dy to get 1/2(ye^y-∫e^y dy) = 1/2(ye^y-e^y) and then 1/2[-x^2e^(-x^2)-e^(-x^2)] This problem got really confusing with all the variables and I just want to make sure that I'm not way off base with my methods and solution. Thanks in advance for any input!