Question

How do you integrate `int 1/ ((x + 1)(x + 2))` using partial fractions?

Answer 1

`= ln (x+1) - ln (x+2) + C`

Explanation:

`color{blue}{1}/ ((x + 1)(x + 2)) = A/(x+1) + B/(x+2)`

`= (color{blue}{A(x+2) + B (x+1)})/((x+1)(x+2))`

let x = -2, B(-2+1) = 1, B = -1
let x = -1, A(-1+2) = 1, A = 1

so the integrand follows

`= int dx qquad 1/(x+1) - 1/(x+2)`

`= ln (x+1) - ln (x+2) + C`