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

johann1301

## 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?

Staff Emeritus
You assumed that ∫ex2dx = ex2/(2x). That's not true.

You do not want to take the route of trying to integrate ex2. No matter how hard you try you will not be able to find that integral. This integral cannot be expressed in terms of elementary functions. You need to take another approach.

Hint: That u-substitution you used to solve ∫xex2dx might come in handy if you use it earlier on.

Last edited:
1 person
johann1301
Solved it. Thanks a lot!