# Thread: Integrating by parts

1. ## Integrating by parts

Can someone help with this, please? I'm realy struggling...

Thanks!

$
\int u^4 e^{\frac{-1}{2}u^2}\ du
$

2. Originally Posted by paolopiace
Can someone help with this, please? I'm realy struggling...

Thanks!

$
\int u^4 e^{\frac{-1}{2}u^2}\ du
$
$\int x^4 e^{-x^2/2} ~ dx = -\int x^3 \left( e^{-x^2/2} \right)' dx$

But, $\int x^3 \left( e^{-x^2/2} \right)' dx = x^3 e^{-x^2/2} - 3\int x^2 e^{-x^2/2} ~ dx$

But, $-\int x^2 e^{-x^2/2} dx = \int x \left( e^{-x^2/2} \right)' dx = xe^{-x^2/2} - \int e^{-x^2/2} ~ dx$

The last one has no primitive.