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This question already has an answer here:

Evaluate the following integral

$\int{\frac{1}{(x+a)(x+b)}}$

(this might involve partial fraction decomposition, $\int{\frac{1}{x^2+x(a+b)+ab}}$ this is what my first step was)

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marked as duplicate by Namaste, egreg, Michael Grant, Micah, Ali Caglayan Nov 20 '14 at 0:08

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When $a \neq b$, we have $$\dfrac1{(x+a)(x+b)} = \dfrac1{b-a}\left(\dfrac1{x+a} - \dfrac1{x+b} \right)$$ Recall that $$\int \dfrac{dx}{x+c} = \ln (\vert x+ c \vert) + \text{constant}$$

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