How do you integrate $(7x + 44)/(x^2 + 10x + 24)$ using partial fractions?

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Answer 1 · 2016-07-06T15:01:05

$= - ln (x+6) + 8 ln (x+4) + C$

$(7x + 44)/(x^2 + 10x + 24)$

$= (7x + 44)/( (x+6)(x+4) ) qquad qquad star$

$= A/(x+6) + B/(x+4)$

$= (A(x+4) + B(x+6) ) /((x+6) (x+4)) qquad qquad square$

so comparing $star$ to $square$

x = -4
7(-4) + 44 = B(-4+6), B = 8

x = -6
7(-6) + 44 = A(-6+4), A = -1

so we have

$int dx qquad -1/(x+6) + 8/(x+4)$

$= - ln (x+6) + 8 ln (x+4) + C$

How do you integrate (7x + 44)/(x^2 + 10x + 24)(7x + 44)/(x^2 + 10x + 24) using partial fractions?