- #1
Ed Aboud
- 201
- 0
Homework Statement
Show using integration by parts that:
[tex] \int x^3 e^x^2 dx = e^x^2 ( \frac{ x^2 -1}{ 2 }) [/tex]
Homework Equations
The Attempt at a Solution
Integration by parts obviously.
[tex] \int u dv = uv - \int v du [/tex]
Let [tex] u = x^3 [/tex] and [tex] dv = e^x^2 dx [/tex]
[tex] \int x^3 e^x^2 dx = \frac{x^2 e^x^2}{ 2 } - \frac{3}{2} \int x e^x^2 dx [/tex]
Now use integration by parts again on [tex] \int x e^x^2 dx [/tex]
And I get :
[tex] \frac{e^x^2}{ 2 } - \frac{1}{2} \int \frac{1}{x} e^x^2 dx [/tex]
This really leaves me no closer again because I have to use integration by parts again on
[tex] \int \frac{1}{x} e^x^2 dx [/tex]
Any suggestions on what to do.
Thanks for the help.