# How do you integrate (2x-1)/((x+1)(x-2)(x+3)) using partial fractions?

Dec 16, 2016

$- \frac{1}{4} \ln \left(x + 1\right) - \ln \left(x - 2\right) + \frac{5}{4} \ln \left(x - 3\right) + c$

#### Explanation:

Before integration, partial fractions can be done as explained below

The partial fractions would thus be

-1/(4(x+1)) -1/(x-2)+5/(4(x-3)

Integration is now simple $- \frac{1}{4} \int \frac{\mathrm{dx}}{x + 1} - \int \frac{\mathrm{dx}}{x - 2} + \frac{5}{4} \int \frac{\mathrm{dx}}{x - 3}$

=$- \frac{1}{4} \ln \left(x + 1\right) - \ln \left(x - 2\right) + \frac{5}{4} \ln \left(x - 3\right) + c$