Rewrite radicals as powers

$\int(3x^{-2}+6x^2)\,dx=-3x^{-1}+2x^3+C=-\frac3x+2x^3+C$, for $x\ne0$.

For $x>0$, divide each term by $x^{1/2}$: $\int(x^{5/2}-x^{3/2}+4x^{1/2}-7x^{-1/2})\,dx=\frac27x^{7/2}-\frac25x^{5/2}+\frac83x^{3/2}-14x^{1/2}+C$. This reproduces the printed answer.