Question

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

Answer 1

`-25/x+C`

Explanation:

We can make use of the integral rule:

`intax^ndx=(ax^(n+1))/(n+1)+C`

However, first we have to put the function into the `ax^n` form.

`(5/x)^2=25/x^2=25x^-2`

The antiderivative of the function is

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