Question

integrate :

(cosec2x) / (1-cot2x)

Answer 1

−∫csc2xdx=−∫1sin2xdx=−∫sec2xtan2xdx=−∫1u2du=−(−1u)+C=cotx+C(u=tanx)−∫csc2⁡xdx=−∫1sin2⁡xdx=−∫sec2⁡xtan2⁡xdx(u=tan⁡x)=−∫1u2du=−(−1u)+C=cot⁡x+C

Answer 2

integral (cosec 2x) = -1/2 log [A(cosec 2x - cot 2x)] = log [A(cosec2x ... The answer is 1/2*ln( cosec(2x) - cot(2x)), not sure why though!