Answer
\[ = \frac{{\,{{\left( {{x^2} + x} \right)}^{11}}}}{{11}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,{{\left( {{x^2} + x} \right)}^{10}}\,\left( {2x + 1} \right)dx} \hfill \\
\hfill \\
set\,\,the\,\,substitution \hfill \\
\hfill \\
u = {x^2} + x\,\,\,\,\,\,\,then\,\,\,\,\,du = \,\left( {2x + 1} \right)dx \hfill \\
\hfill \\
thererore \hfill \\
\hfill \\
\int_{}^{} {{u^{10}}du} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \frac{{{u^{11}}}}{{11}} + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,u = {x^2} + x \hfill \\
\hfill \\
= \frac{{\,{{\left( {{x^2} + x} \right)}^{11}}}}{{11}} + C \hfill \\
\hfill \\
\end{gathered} \]
