$\displaystyle \int \frac{dx}{2x^{\frac{1}{3}} + \sqrt{x}}$

let x = z^3

dx = 3z^2dz

$\displaystyle \int \frac{dx}{2z + z^{\frac{3}{2}}}$

$\displaystyle \int \frac{3z^2dz}{2z + z^{\frac{3}{2}}}$

$\displaystyle \int \frac{3z}{2+z^\frac{1}{2}}dz$

im stuck here

.... divide numerator by denominator

$\displaystyle \int 3z^{\frac{1}{2}} - 6 + \frac{12}{2+z^{\frac{1}{2}}}dz$

im stuck at the integral of 12 / (2 + z^(1/2))