Answer
$$\frac{{{{\left( {2x + 3} \right)}^6}}}{{56}}\left( {4x - 1} \right) + C$$
Work Step by Step
$$\eqalign{
& \int {x{{\left( {2x + 3} \right)}^5}} dx \cr
& {\text{Integrate by tables using the formula 95}} \cr
& \int {x{{\left( {ax + b} \right)}^n}dx} = \frac{{{{\left( {ax + b} \right)}^{n + 1}}}}{{{a^2}}}\left( {\frac{{ax + b}}{{n + 2}} - \frac{b}{{n + 1}}} \right) + C,\,\,n \ne - 1,\,\, - 2 \cr
& {\text{Therefore,}} \cr
& \int {x{{\left( {2x + 3} \right)}^5}} dx = \frac{{{{\left( {2x + 3} \right)}^{5 + 1}}}}{{{2^2}}}\left( {\frac{{2x + 3}}{{5 + 2}} - \frac{3}{{5 + 1}}} \right) + C \cr
& {\text{Simplifying}} \cr
& \int {x{{\left( {2x + 3} \right)}^5}} dx = \frac{{{{\left( {2x + 3} \right)}^6}}}{4}\left( {\frac{{2x + 3}}{7} - \frac{1}{2}} \right) + C \cr
& \int {x{{\left( {2x + 3} \right)}^5}} dx = \frac{{{{\left( {2x + 3} \right)}^6}}}{4}\left( {\frac{{4x + 6 - 7}}{{14}}} \right) + C \cr
& \int {x{{\left( {2x + 3} \right)}^5}} dx = \frac{{{{\left( {2x + 3} \right)}^6}}}{{56}}\left( {4x - 1} \right) + C \cr} $$
