Question Number 20451 by tammi last updated on 27/Aug/17
$$\int{sin}^{\mathrm{3}} {x}\mathrm{cos}\:^{\mathrm{4}} {xdx} \\ $$
Answered by mrW1 last updated on 27/Aug/17
$$=−\int{sin}^{\mathrm{2}} {x}\mathrm{cos}\:^{\mathrm{4}} {xd}\left(\mathrm{cos}\:{x}\right) \\ $$$$=−\int\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \:{x}\right)\mathrm{cos}\:^{\mathrm{4}} {xd}\left(\mathrm{cos}\:{x}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{7}}\mathrm{cos}^{\mathrm{7}} \:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cos}^{\mathrm{5}} \:\mathrm{x}+\mathrm{C} \\ $$