1. ## Integral

Hi,

How to i find the integral:

dx/((x+1)*(1+x^2)^(0.5))

2. Originally Posted by omerbgu
Hi,

How to i find the integral:

dx/((x+1)*(1+x^2)^(0.5))
If the problem is

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

Make two substitutions, first $x = \tan \theta$ this will give

$\int \frac{d \theta}{ \sin \theta + \cos \theta}$

Next, let $\theta = 2 \tan^{-1} z$, this gives

$-2 \int \frac{dz}{z^2-2z-1}$

Which you should be able to do. Of course you could combine the substitutions.

3. Thanks!