Math Help - Integration by Parts (with Substitution)

1. Integration by Parts (with Substitution)

I'm trying to do a problem that is integration by parts.

$\int {x}^{3}{e}^{{x}^{2}}/{({x}^{2}+1)}^{2} dx$

I'm pretty sure I need to do a substitution, like make $g={x}^{2}$ but I'm not sure.

If that is the case, I'm not sure where to go next. What should be my u and what should be my dv?

Thanks,

MJ

2. As you said, substitute $t=x^2$ to get:

$\frac{1}{2} \, \int \frac{t e^t}{(t+1)^2} \, dt$

Use integraton by parts with $u=t e^t$ and $dv=\frac{dt}{(t+1)^2}$

Can you do that ?

3. I have no idea how you went through the steps to get that. How did you get rid of the x^3?

Also, thank you for the reply...

4. $x^3 = x^2 \cdot x$ ..