# Math Help - really stuck on this integral

1. ## really stuck on this integral

use a trigonometric substitution to find integral of 1/(1+3x^2)^3/2 between limits 0 and 1.

I think you have to use tan or sin not quite sure how though.

2. Originally Posted by i_zz_y_ill
use a trigonometric substitution to find integral of 1/(1+3x^2)^3/2 between limits 0 and 1.

I think you have to use tan or sin not quite sure how though.
let $\sqrt 3x = \tan \theta$

now continue with the substitution process

we use tan because we are using the $1 + \tan^2 (x) = \sec^2 x$

3. ## how does that work,

thanks but cant see how that works. No doubt ur wright but I still can't do it..

4. You can leave $x=\frac{1}{\sqrt{3}}tan({\theta}), \;\ dx=\frac{1}{\sqrt{3}}sec^{2}{\theta}d{\theta}$

This changes your limits of integration to 0 to Pi/3.

Making the subs will whittle it down to:

$\frac{1}{\sqrt{3}}\int_{0}^{\frac{\pi}{3}}{cos{\th eta}}d{\theta}$