∫secxcosecx2cotx-secxcosecxdx=
logsecx+tanx+c
logsecx+cosecx+c
12logsec2x+tan2x+c
logsec2x+cosec2x+c
logsec2x.cosec2x+c
Explanation for correct option:
Evaluate : ∫secxcosecx2cotx-secxcosecxdx
Consider the given Equation as
I=∫secxcosecx2cotx-secxcosecxdxI=∫1sinx.cosxdx2cosxsinx-1cosx.sinxI=∫12cos2-1dxI=∫1cos2xdxwhere,2cos2-1=cos2xI=∫sec2xdxwhere,1cos2x=sec2xI=12logsec2x+tan2x+c
Hence the correct answer is Option C.