# Evalute The Following Integral. (1)

• Feb 16th 2010, 01:11 PM
TWiX
Evalute The Following Integral. (1)
Hello :D
here is it :
$\displaystyle \int \frac{ x e^x }{ \sqrt{e^x+1} }dx$.

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

any ideas??
• Feb 16th 2010, 01:17 PM
Drexel28
Quote:

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

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

any ideas??

$\displaystyle \ln(z)=x$ then $\displaystyle \sqrt{z+1}=m$
• Feb 16th 2010, 01:18 PM
General
Quote:

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

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

any ideas??

use $\displaystyle x=ln(t)$ to get:

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

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

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

two quick "by parts" will kill it.