Answer
$\dfrac{3x^{2}}{10}-\dfrac{3}{5} \ln |x|+C$
Work Step by Step
We are given that $I=\int (\dfrac{3x}{5}-\dfrac{3}{5x}) \ dx$
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 $\int (\dfrac{3x}{5}-\dfrac{3}{5x}) \ dx =\dfrac{3}{5} [\int x \ dx -\int \dfrac{1}{x} \ dx ]$
or, $= \dfrac{3x^{2}}{10}-\dfrac{3\ln |x|}{5}+C$
or, $=\dfrac{3x^{2}}{10}-\dfrac{3}{5} \ln |x|+C$
