Question Number 82391 by jagoll last updated on 21/Feb/20
$$\int\:\mathrm{sin}\:{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$
Commented by M±th+et£s last updated on 21/Feb/20
$${i}\:{think}\:{that}\:{its}\:{special}\:{integral} \\ $$$${cos}\left({sin}\left({x}\right)\right)=\mathrm{1}−\frac{{sin}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}{i}}+\frac{{sin}^{\mathrm{4}} \left({x}\right)}{\mathrm{4}{i}}−\frac{{sin}^{\mathrm{6}} \left({x}\right)}{\mathrm{6}{i}}+… \\ $$$${I}=\int\left({sin}\left({x}\right)−\frac{{sin}^{\mathrm{3}} \left({x}\right)}{\mathrm{2}{i}}+\frac{{sin}^{\mathrm{5}} \left({x}\right)}{\mathrm{4}{i}}−\frac{{sin}^{\mathrm{7}} \left({x}\right)}{\mathrm{7}{i}}+…\right){dx} \\ $$