Question Number 136971 by Eric002 last updated on 28/Mar/21
$$\int{csc}^{\mathrm{4}} \left({x}\right)\:{cot}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$
Answered by Ñï= last updated on 28/Mar/21
$$\int{csc}\:^{\mathrm{4}} {x}\mathrm{cot}\:^{\mathrm{2}} {xdx}=−\int\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right)\mathrm{cot}\:^{\mathrm{2}} {xd}\left(\mathrm{cot}\:{x}\right) \\ $$$$=−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{cot}^{\mathrm{3}} \:{x}−\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cot}\:^{\mathrm{5}} {x}+{C} \\ $$