Answer
$\dfrac{1}{22 } (x^2+4)^{11}+C$
Work Step by Step
We are given that $I=\int x (x^2+4)^{10} \ dx$
Let us consider that $u=x^2+4 \implies dx=\dfrac{du}{2x}$
Now, we have $I= \int x u^{10} \times (\dfrac{du}{2x})$
or, $=\dfrac{1}{2} \int u^{10} \ du$
or, $=\dfrac{1}{2} \dfrac{u^{11}}{11} +C$
or, $=\dfrac{1}{22 } (x^2+4)^{11}+C$
