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

Feb 24, 2016

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:

$\frac{{x}^{2} + 2}{x + 3} = x - 3 + \frac{11}{x + 3}$

This may be integrated term by term.

$\int \frac{{x}^{2} + 2}{x + 3} \mathrm{dx} = \int \left(x - 3 + \frac{11}{x + 3}\right) \mathrm{dx}$

$= {x}^{2} / 2 - 3 x + 11 \ln \left\mid x + 3 \right\mid + C$