$\int \frac{\mathrm{dx}}{(2\mathrm{x}+1{)}^{5/6}(3\mathrm{x}+5{)}^{\frac{7}{6}}}=$

$$\begin{gathered} \int \frac{\mathrm{dx}}{(2\mathrm{x}+1{)}^{5/6}(3\mathrm{x}+5{)}^{\frac{7}{6}}}=\int \frac{\mathrm{dx}}{\left({\displaystyle \frac{2\mathrm{x}+1}{3\mathrm{x}+5}}{)}^{5/6}\right(3\mathrm{x}+5{)}^2} \\ =\frac{1}{7}\int \frac{\mathrm{dx}}{({\displaystyle t}{)}^{5/6}} put \frac{2\mathrm{x}+1}{3\mathrm{x}+5}=t\Rightarrow \frac{dx}{{\left(3\mathrm{x}+5\right)}^2}=\frac{dt}{7} \\ =\frac{6}{7}{\left(\frac{2\mathrm{x}+1}{3\mathrm{x}+5}\right)}^{\frac{1}{6}}+c \end{gathered}$$