Question

How do you integrate `(2x) / (4x^2 + 12x + 9)` using partial fractions?

Answer 1

`=1/2ln|2x+3|+3/(2(2x+3))+C`.
You don't use partial fractions, because the denominator is a perfect square.

Explanation:

`int (2x)/(4x^2+12x+9)dx`
`=int(2x)/(2x+3)^2dx`
So substitute `u=2x+3`, `dx=(du)/2`:
`=1/2int (u-3)/u^2du`
`=1/2intu^-1-3u^-2dx`
`=1/2ln|2x+3|+3/(2(2x+3))+C`