# Math Help - Evalute The Following Integral. (1)

1. ## Evalute The Following Integral. (1)

Hello
here is it :
$\int \frac{ x e^x }{ \sqrt{e^x+1} }dx$.

by parts would be an idea.
but it really hard to apply the integration by parts directly.

any ideas??

2. Originally Posted by TWiX
Hello
here is it :
$\int \frac{ x e^x }{ \sqrt{e^x+1} }dx$.

by parts would be an idea.
but it really hard to apply the integration by parts directly.

any ideas??
$\ln(z)=x$ then $\sqrt{z+1}=m$

3. Originally Posted by TWiX
Hello
here is it :
$\int \frac{ x e^x }{ \sqrt{e^x+1} }dx$.

by parts would be an idea.
but it really hard to apply the integration by parts directly.

any ideas??
use $x=ln(t)$ to get:

$\int \frac{ln(t)}{\sqrt{t+1}}dt$.

use $t+1=w^2$ to get:

$2\int ln(w^2-1) dw = 2\int ln(w+1) dw + 2 \int ln(w-1) dw$.

two quick "by parts" will kill it.