need help: integration problem?

Question

integrate {(x-2)/[(x-3)^2(x+2)]} dx

Answer 1

Integrate {(x-2)/[(x-3)^2(x+2)]} with respect to x.

First rearrange the terms to make it easier to integrate. Use partial fraction decomposition to break apart the fraction.

(x-2)/[(x-3)^2(x+2)] = a/(x+2) + b/(x-3) + c/(x-3)³
Solving for a, b, and c we get
a = -4/25
b = 4/25
c = 1/5

Now we can integrate.

∫{(x-2)/[(x-3)^2(x+2)]}dx
= ∫{(-4/25)/(x+2) + (4/25)/(x-3) + (1/5)/(x-3)²}dx
= (-4/25)ln(x + 2) + (4/25)ln(x - 3) - (1/5)/(x - 3) + C
= (4/25){ln(x - 3) - ln(x + 2)} - (1/5)/(x - 3) + C

Answer 2

I get

(4/25)*(ln(x-3) - ln(x+2)) - 1/(5*(x-3)) +C


Doug

Answer 3

the answer is
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