Question

\[\int \sec x\]

Answer 1

proof without using the rationalising by tan x and sec x
\[\int\sec x=\ln (\tan x +\sec x)+c\]

Answer 2

Try partial fractions. secx=1/cosx=cosx/cos^2(x)=cosx/(1-sin^2(x))
Then do a substitution u=sinx. Do partial fractions the show that the result is the same