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

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Answer 1 · 2016-02-07T21:35:18

$-25/x+C$

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

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

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