\int x^{2}\left(2x^{3}+4\right)^{5}\mathrm{d}x=\dfrac{1}{6}\int6x^{2}\left(2x^{3}+4\right)^{5}\mathrm{d}x=\dfrac{1}{6}\cdot\dfrac{\left(2x^{3}+4\right)^{6}}{6}+C