# How do you use partial fraction decomposition to decompose the fraction to integrate (2x)/ (4x^2 + 12x + 9)?

Jul 29, 2015

$\frac{2 x}{4 {x}^{2} + 12 x + 9} = \frac{1}{2 x + 3} - \frac{3}{2 x + 3} ^ 2$

#### Explanation:

$\frac{2 x}{4 {x}^{2} + 12 x + 9} = \frac{2 x}{2 x + 3} ^ 2$

$= \frac{2 x + 3 - 3}{2 x + 3} ^ 2$

$= \frac{2 x + 3}{2 x + 3} ^ 2 - \frac{3}{2 x + 3} ^ 2$

$= \frac{1}{2 x + 3} - \frac{3}{2 x + 3} ^ 2$