Question

How do you integrate `int (x²+2) / (x+3)` using partial fractions?

Answer 1

Before using partial fractions make sure that the degree of the numerator is less than that of the denominator. If it's not, then do the division first.

Explanation:

By division:

`(x^2+2)/(x+3) = x-3+11/(x+3)`

This may be integrated term by term.

`int (x^2+2)/(x+3) dx = int (x-3+11/(x+3))dx`

`= x^2/2-3x+11ln abs(x+3) +C`