Question Number 169640 by MikeH last updated on 05/May/22
$$\int\mathrm{cos}\left({x}^{\mathrm{7}} \right){dx}\:= \\ $$
Commented by mkam last updated on 05/May/22
$$ \\ $$$$=\:\int\:\Sigma\:\left(−\mathrm{1}\right)^{{n}} \:×\:\frac{{x}^{\mathrm{14}{n}} }{\left(\mathrm{2}{n}\right)!}\:{dx}\:=\:\Sigma\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}\right)!}\:\int\:{x}^{\mathrm{14}{n}} \:{dx} \\ $$$$ \\ $$$$=\:\Sigma\frac{\left(−\mathrm{1}\right)^{{n}} \:.\:{x}^{\mathrm{14}{n}+\mathrm{1}} }{\left(\mathrm{14}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}\right)!}\:+{C} \\ $$