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#