# How do you integrate #int 1 / ((x+5)^2 (x-1) ) # using partial fractions?

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Trevor Ryan.
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Sep 20, 2016

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Since the denominator has been factorized as a combination of linear factors, one repeated, we may write it in partial fraction form as :

By comparing terms in the numerator, we now see that :

Solving this system of linear equations yields :

Hence the original integral may be written and solved as follows :

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