Answer
$3 \ln |x|- \dfrac{x^{2}}{2}+c$
Work Step by Step
Calculate the anti-derivative.
Since, we know $\int x^{n} dx=\dfrac{x^{n+1}}{n+1}+c$ and $ \int \dfrac{1}{x} dx=\ln |x|+c$
where $c$ is a constant of proportionality.
Then $\int (\dfrac{3}{x}-x) dx=3 \int \dfrac{1}{x} dx-\int x dx dx$
or, $=3 \ln |x|- \dfrac{x^{1+1}}{1+1}+c$
Thus, $=3 \ln |x|- \dfrac{x^{2}}{2}+c$
