Answer
$\dfrac{4x^{3}}{5}+\dfrac{4}{5x}+C$
Work Step by Step
We are given that $I=\int (\dfrac{4x^2}{5}-\dfrac{4}{5x^2}) \ dx$
In order to solve the above integral, we will use the following formula such as:
$\int x^n \ dx=\dfrac{x^{n+1}}{n+1}+C$
Now, we have $\int (\dfrac{4x^2}{5}-\dfrac{4}{5x^2}) \ dx =\int (\dfrac{4x^2}{5}-\dfrac{4}{5}x^{-2}) \ dx$
or, $= \dfrac{4x^{3}}{5}-\dfrac{4x^{-2}}{(5)(-1)}+C$
or, $=\dfrac{4x^{3}}{5}+\dfrac{4}{5x}+C$
