Question Number 59905 by Sardor2211 last updated on 15/May/19
$$\int\left(\mathrm{2x}−\mathrm{1}\hat {\right)}\mathrm{20} \\ $$
Commented by maxmathsup by imad last updated on 16/May/19
$${if}\:{you}\:{mean}\:{I}\:=\int\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{20}} {dx}\:\Rightarrow{I}\:=\int\:\sum_{{k}=\mathrm{0}} ^{\mathrm{20}} \:{C}_{\mathrm{20}} ^{{k}} \:\left(\mathrm{2}{x}\right)^{{k}} \left(−\mathrm{1}\right)^{\mathrm{20}−{k}} \:{dx} \\ $$$$=\sum_{{k}=\mathrm{0}} ^{\mathrm{20}} \:\:\mathrm{2}^{{k}} \:\left(−\mathrm{1}\right)^{\mathrm{20}−{k}} \:\:{C}_{\mathrm{20}} ^{{k}} \:\int\:\:{x}^{{k}} \:{dx} \\ $$$$=\sum_{{k}=\mathrm{0}} ^{\mathrm{20}} \:\mathrm{2}^{{k}} \left(−\mathrm{1}\right)^{{k}} \:{C}_{\mathrm{20}} ^{{k}} \:\:\frac{\mathrm{1}}{{k}+\mathrm{1}}\:+{C} \\ $$