∫cot3xdx=

I=∫cot3⁡xdx=∫cot2⁡xcot⁡xdx I=∫cosec2⁡x−1cot⁡xdx=∫cot⁡xcosec2⁡xdx−∫cot⁡xdx Let I1=∫cot⁡xcosec2⁡xdxcot⁡x=t→−cosec2⁡xdx=dtI1=∫tdt=−t22I=−(cot⁡x)22−log⁡|sin⁡x|+C