Интеграл dx/(x*(lnx+1)^1/3)

[latex]\int \frac{dx}{x\cdot (lnx+1)^{\frac{1}{3}}}=\int \frac{\frac{dx}{x}}{(lnx+1)^{\frac{1}{3}}}=[\, t=lnx+1,\; dt=\frac{dx}{x}\, ]=\\\\\\=\int \frac{dt}{t^{\frac{1}{3}}}=\int t^{-\frac{1}{3}}\, dt=\frac{t^{\frac{2}{3}}}{\frac{2}{3}}+C=\frac{3}{2}\cdot (lnx+1)^{\frac{2}{3}}+C=\\\\=\frac{3}{2}\cdot \sqrt[3]{(lnx+1)^2}+C[/latex]