Question

\[\int \frac{1}{\sqrt x - \sqrt[3]{x}} dx\]
\[u=\sqrt[6]{x}\]
\[du=6u^5 dx\]
\[\int\frac{6u^5}{u^3 - u^2} du\]
\[\int \frac{6u^3}{(u-1)} du\]
\[6\int \frac{u^3}{(u-1)} du\]

Answer 1

Long division
\[u^2 +u+1+\frac{1}{u-1}\]

Answer 2

according to wolf, my long division is wrong

Answer 3

wait

Answer 4

Yaaay I'm right