Evaluate: ∫ (dx)/(x^(1/2) - x^(1/3)).

Let $x = t^6$, $6t^5\,dt = dx$ $6\int \frac{t^5}{t^3 - t^2}\,dt = 6\int\left(t^2 + t + 1 + \frac{1}{t-1}\right)dt$ $= 6\left[\frac{t^3}{3} + \frac{t^2}{2} + t + \log(t-1)\right] + c$ $= 6\left[\frac{1}{3}\sqrt{x} + \frac{1}{2}\sqrt[3]{x} + x^{1/6} + \log\left(x^{1/6} - 1\right)\right] + c$