Evaluate: ∫ (dx)/(⁴√((x-1)³ (x+2)⁵)).

$\int\frac{dx}{\sqrt[4]{(x-1)^3(x+2)^5}} = \int\left(\frac{x-1}{x+2}\right)^{-3/4}\times\frac{1}{(x+2)^2}\,dx$ let $\frac{x-1}{x+2} = t$, $\frac{3}{(x+2)^2}\,dx = dt$ $\therefore I = \frac{1}{3}\int t^{-3/4}\,dt = \frac{4}{3}t^{1/4} = \frac{4}{3}\left(\frac{x-1}{x+2}\right)^{1/4} + c$