# What is the antiderivative of  (5/x)^2?

Feb 7, 2016

$- \frac{25}{x} + C$

#### Explanation:

We can make use of the integral rule:

$\int a {x}^{n} \mathrm{dx} = \frac{a {x}^{n + 1}}{n + 1} + C$

However, first we have to put the function into the $a {x}^{n}$ form.

${\left(\frac{5}{x}\right)}^{2} = \frac{25}{x} ^ 2 = 25 {x}^{-} 2$

The antiderivative of the function is

int25x^-2dx=(25x^(-2+1))/(-2+1)+C=(25x^-1)/(-1)+C=color(red)(-25/x+C