how can i integrate Sec(x)/2 and cosec(x)/2?

Question

how can i integrate Sec(x)/2 and cosec(x)/2 ? explain me.

Answer 1

sec x=(secx+tanx)(secx)/(secx+tanx)
=(sec^2x+secxtanx)/(secx+tanx)
now the Nr. is the differential coefficient of the Dr.
the integral will be log(secx+tanx)+C
so int secx/2=1/2 log(secx+tanx)+C
similarly for cosecx multiply the Nr. and the Dr by cosecx+cotx

Answer 2

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Answer 3

the one above is right but the real answer is 1/2 ln(secx+tanx)+C not 1/2 log(secx+tanx)+C