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Find the integral of 2/((2-x)(x+2)^2)dx.

2 answers

I tried to use partial fractions to do it, but it didn't work.
Of course it works. Why don't you show your work and the reason why you rejected it?

2/((2-x)(x+2)^2) = (1/8) (1/(x+2) + 4/(x+2)^2 - 1/(x-2))

So, the integral is just

(1/8) (ln(x+2) - 4/(x+2) - ln(x-2))
= (1/8) (ln((x+2)/(x-2)) - 4/(x+2)) + C
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