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

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

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Answer 1 · 2016-12-28T14:48:49

$=1/2ln|2x+3|+3/(2(2x+3))+C$ .
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 $u=2x+3$ , $dx=(du)/2$ :
$=1/2int (u-3)/u^2du$
$=1/2intu^-1-3u^-2dx$
$=1/2ln|2x+3|+3/(2(2x+3))+C$

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

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