(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Substitution method with Integration by Parts?

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