Question Number 152502 by Tawa11 last updated on 29/Aug/21
$$\int\:\mathrm{9x}^{\mathrm{2}} \left(\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{3}\right)^{\mathrm{10}} \:\mathrm{dx} \\ $$
Answered by Olaf_Thorendsen last updated on 30/Aug/21
$$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{9}{x}^{\mathrm{2}} \left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{10}} \:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\mathrm{3}^{\mathrm{12}} \int\underset{{k}=\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\mathrm{C}_{{k}} ^{\mathrm{10}} \left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{{k}} {x}^{\mathrm{2}{k}+\mathrm{2}} \:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\mathrm{3}^{\mathrm{12}} \underset{{k}=\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\mathrm{C}_{{k}} ^{\mathrm{10}} \left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{{k}} \frac{{x}^{\mathrm{2}{k}+\mathrm{3}} }{\mathrm{2}{k}+\mathrm{3}}+\mathrm{C} \\ $$
Commented by Tawa11 last updated on 30/Aug/21
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$