# Integrate 1/((x-1)(x+2)) from 2 to 5

## Answer

$\frac{62}{225}$

## Step-by-step explanation

Problem

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

1

Using partial fraction decomposition, the fraction $\frac{1}{\left(2+x\right)\left(x-1\right)}$ can be rewritten as

$\frac{1}{\left(2+x\right)\left(x-1\right)}=\frac{A}{2+x}+\frac{B}{x-1}$

## Answer

$\frac{62}{225}$