# Thread: [SOLVED] Help with trigonometric substitution

1. ## [SOLVED] Help with trigonometric substitution

$\int\ (dx/4+x^{2})^{2}$
dont know how to do this problem without the square root

2. Originally Posted by vinson24
$\int\ (dx/4+x^{2})^{2}$
dont know how to do this problem without the square root
Are you sure it's not

$\int{\frac{dx}{(4 + x^2)^2}}$?

3. Yes that's how you write it sorry

4. $\int{\frac{dx}{(4 + x^2)^2}}$

$x = 2\tan{t}$

$dx = 2\sec^2{t} \, dt$

$\int \frac{2\sec^2{t}}{(4 + 4\tan^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{\sec^2{t}}{(1 + \tan^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{\sec^2{t}}{(\sec^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{1}{\sec^2{t})} \, dt$

$\frac{1}{8} \int \cos^2{t} \, dt$

take it from here?