$$\begin{eqnarray*} \int (2x^{1/3}+5x^{-1})\,dx &=& \int 2x^{1/3}\,dx+\int \dfrac{5}{x}\,dx=2\int x^{1/3}\,dx+5\int \dfrac{1}{x}\,dx \\ &=& 2\cdot {\dfrac{{x^{4/3}}}{{{\dfrac{{4}}{{3} }}}}}+{5\ln \,}\vert x\vert +C={\dfrac{{3x^{4/3}}}{{2}}}+5\ln \,\vert x\vert +C \end{eqnarray*}$$