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

1. Oct 10, 2013

johann1301

1. The problem statement, all variables and given/known data

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?

2. Oct 10, 2013

D H

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: Oct 10, 2013
3. Oct 10, 2013

johann1301

Solved it. Thanks a lot!

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