# How do you integrate int (3x)/sqrt((1-x^2))dx using trigonometric substitution?

Jan 24, 2016

You need to use the beautiful Pythagorean right triangle.

Here is the general antiderivative :
$- 3 \cdot \sqrt{1 - {x}^{2}}$

#### Explanation:

Here's a quick paint job to show you the lovely right triangle:

You now need to find the following:

1)x

2)dx/(d theta)

3)sqrt(1-x^2)

I'll give you a gentle and loving push in the right direction:

What is x?

Well, it sure looks to be :

$x = \sin \left(\theta\right)$