# Thread: Integral3

1. ## Integral3

$\int \frac{\sqrt{x}dx}{(1+x)^2}$

2. Originally Posted by Apprentice123
$\int \frac{\sqrt{x}dx}{(1+x)^2}$
let $u = \sqrt{x}$. this substitution yields,

$2 \int \frac {u^2}{(1 + u^2)^2}~du = 2 \int \frac {u^2 + 1 - 1}{(1 + u^2)^2}~du = 2 \Bigg[ \int \frac 1{1 + u^2}~du - \int \frac 1{(1 + u^2)^2}\Bigg]$

the first integral in brackets is easy, it is just the arctangent. for the second, do a trig substitution to finish it off. $u = \tan \theta$