Asked by Henry
Find the integral of 2/((2-x)(x+2)^2)dx.
Answers
Answered by
Henry
I tried to use partial fractions to do it, but it didn't work.
Answered by
Steve
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
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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