Evaluate the integral (using partial fractions maybe?)

Question

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)

Answer 1

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