# Evaluate the integral. \int_{2}^{\infty}\frac{dx}{(x+2)^{2}}

Evaluate the integral.
${\int }_{2}^{\mathrm{\infty }}\frac{dx}{{\left(x+2\right)}^{2}}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Laith Petty
Step 1
The given improper integral is,
${\int }_{2}^{\mathrm{\infty }}\frac{dx}{{\left(x+2\right)}^{2}}$
Step 2
Evaluate the integral using substitution as follows.
${\int }_{2}^{\mathrm{\infty }}\frac{dx}{{\left(x+2\right)}^{2}}={\int }_{2}^{\mathrm{\infty }}\frac{1}{{u}^{2}}du$ [Substitute u=x+2]
$={\int }_{2}^{\mathrm{\infty }}{u}^{-2}du$
$={\left[\frac{-1}{u}\right]}_{2}^{\mathrm{\infty }}$
$=\frac{-1}{\left(\mathrm{\infty }+2\right)}+\left(\frac{1}{2+2}\right)$ [Back substitute u]
$=\frac{1}{4}$
###### Not exactly what you’re looking for?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee