How to integrate x^3*e^(x^2) ?

Question

integral x^3*e^(x^2) dx

im confused what do after i substitute u = x^2

I get (1/2)integral u*e^u du
do I do parts now?

thanks

Answer 1

Yep, from there it is a standard and fairly easy integration by parts.

(1/2) ∫ u.e^u du
= (1/2) (u e^u - ∫1.e^u du) where we differentiate u and integrate e^u du
= (1/2) (u e^u - e^u + c)
= (1/2) e^(x^2) (x^2 - 1) + c

Answer 2

Let dv = e^(x^2) and u = x^3
Do parts three times, tabular integration will help here.
http://en.wikipedia.org/wiki/Integration_by_parts
http://www.maa.org/pubs/Calc_articles/ma035.pdf