• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter johann1301
  • Start date
  • #1
217
1

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?
 

Answers and Replies

  • #2
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
683
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:
  • Like
Likes 1 person
  • #3
217
1
Solved it. Thanks a lot!
 

Related Threads on Integrate (x^3)(e^(x^2))

  • Last Post
Replies
12
Views
52K
Replies
8
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
1
Views
3K
Top