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**1. 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]

**2. Homework Equations**

**3. 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.