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

## Answer

$0.2877$

## Step-by-step explanation

Problem to solve:

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

1

Rewrite the fraction $\frac{1}{x\left(x+1\right)}$ in $2$ simpler fractions using partial fraction decomposition

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

## Answer

$0.2877$