Thread: Need help solving simple integral

Wolfram Alpha gives an answer of $\displaystyle \frac{1}{2}$, but it doesn't give the steps. Can someone walk me through the problem or a similar problem? I believe I need to use integration by parts but I keep getting stuck.

Thanks

$\displaystyle \int_{0}^{\infty}\frac{3x}{(1+x)^{4}}dx$

Originally Posted by downthesun01

Wolfram Alpha gives an answer of $\displaystyle \frac{1}{2}$, but it doesn't give the steps. Can someone walk me through the problem or a similar problem? I believe I need to use integration by parts but I keep getting stuck.

Thanks

$\displaystyle \int_{0}^{\infty}\frac{3x}{(1+x)^{4}}dx$

try the substitution $\displaystyle u = x+1$

Thanks. I just got it myself using integration by parts.

$\displaystyle u=3x$, $\displaystyle du=3dx $, $\displaystyle dv=\frac{1}{(1+x)^{4}}$, $\displaystyle v\frac{-1}{3(1+x)^{-3}}$