Question

Integrate...

Answer 1

\[\int\limits_{}^{}\frac{\sqrt[3]{x}}{\sqrt[3]{x}-1}dx\]

Answer 2

Use the substitution\[u=x^{1/3}\]\[du=\frac{1}{3}x^{-2/3}dx\to dx=3x^{2/3}du=3u^2du\]then our integral becomes\[3\int\frac{u^3}{u-1}du\]which we can perform long division on, then integrate.

Answer 3

Ohhh thank you :)