Question Number 79500 by ubaydulla last updated on 25/Jan/20
$$\int\left(\mathrm{cot}\:^{\mathrm{2}} {x}+\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$
Answered by john santu last updated on 25/Jan/20
$$\int\mathrm{cot}\:^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right){dx}\:= \\ $$$$\int\mathrm{cot}\:^{\mathrm{2}} {x}\:\mathrm{cosec}\:^{\mathrm{2}} {xdx}= \\ $$$$\int−\mathrm{cot}\:^{\mathrm{2}} {x}\:{d}\left(\mathrm{cot}\:{x}\right)\:= \\ $$$$−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{cot}\:^{\mathrm{3}} {x}\:+\:{c} \\ $$