Integrate (x^3)(e^(x^2))

Homework Statement

Use both substitution and integration by parts to solve:

∫x3ex2dx

2. The attempt at a solution

∫x3ex2dx

∫ex2x3dx

(1/2x)ex2x3-∫(1/2x)ex23x2dx

(1/2)ex2x2-(3/2)∫ex2xdx

(ex2x2/2)-(3/2)∫eux(du/2x)

(ex2x2/2)-(3/2)(1/2)∫eudu

(ex2x2/2)-(3/4)eu + C

(ex2x2/2)-(3/4)ex2 + C

The solution is supposed to be; (ex2x2/2)-(1/2)ex2 + C

Where am i going wrong?

D H
Staff Emeritus