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

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Answer 1 · 2015-07-29T01:46:47

$(2x)/ (4x^2 + 12x + 9) = 1/(2x+3) - 3/(2x+3)^2$

$(2x)/ (4x^2 + 12x + 9) = (2x)/(2x+3)^2$

$= (2x+3-3)/(2x+3)^2$

$= (2x+3)/(2x+3)^2 -3/(2x+3)^2$

$= 1/(2x+3) - 3/(2x+3)^2$

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