Answer
$\frac{2}{3}(x^3-1)^{3/2}+C$
Work Step by Step
Let $u=x^3-1=>du=3x^2dx=>\frac{1}{3}du=x^2dx$
=$\int \sqrt{\frac{x^4}{x^3-1}}dx$
=$\int \frac{x^2}{\sqrt{x^3-1}}dx$
=$\int \frac{1}{\sqrt{u}}\frac{1}{3}du$
=$\frac{1}{3} \int U^{-1/2}du$
=$\frac{2}{3}u^{1/2}+C$
=$\frac{2}{3}(x^3-1)^{3/2}+C$
