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