Question

 

$int{sinx/sqrt[3]{cos^2x} dx$

Answer 1

$int frac{sinx}{sqrt[3]{cos^2x}}dx=int (cosx)^{-frac{2}{3}}cdot sinxcdot dx=[t=cosx,dt=-sinxdx]=\\=-int t^{-frac{2}{3}}cdot dt=-frac{t^{frac{1}{3}}}{frac{1}{3}}+C=-3(cosx)^{frac{1}{3}}+C=-3sqrt[3]{cosx}+C$