Find the integral : $\int\frac{dx}{x^\frac{1}{2}+x^\frac{1}{3}}$ Find the integral : $\int\dfrac{dx}{x^\frac{1}{2}+x^\frac{1}{3}}$
Please guide which substitution fits in this I am not getting any clue on this .. thanks..

After using the substitution posted you'll have to do a bit of work but should get this at your final answer
$$2\sqrt{x}+\ln(\sqrt{x}-1)-\ln(\sqrt{x}+1)-\ln(x-1)-3x^\frac{1}{3}+\ln(x^\frac{2}{3}+x^\frac{1}{3}+1)-2\ln(x^\frac{1}{3}-1)-\ln(x^\frac{1}{3}+x^\frac{1}{6}+1)+2\ln(x^\frac{1}{6}-1)+\ln(x^\frac{1}{3}-x^\frac{1}{6}+1)-2\ln(x^\frac{1}{6}+1)+6x^\frac{1}{6}$$
