Question Number 18281 by aplus last updated on 17/Jul/17
Answered by Tinkutara last updated on 18/Jul/17
$$\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{sin}\:\mathrm{2}{x}\:{dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{−\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}\right)\:=\:\frac{−\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{4}}\:+\:{C} \\ $$
Answered by mrW1 last updated on 18/Jul/17
$$=\int\mathrm{sin}\:\mathrm{x}\:\mathrm{d}\left(\mathrm{sin}\:\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}+\mathrm{C} \\ $$