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Question
Evaluate the following integrals:
Solution
`"sec x"/("sec"(2"x")) = ("cos"(2"x"))/"cos x"`
`= (2 "cos"^2"x" - 1)/"cos x"`
`= ("2 cos"^"x")/"cos x" - 1/"cos x"`
= 2 cos x - sec x
`int ("sec"("x"))/("sec"(2"x")) "dx" = int[2 "cos x" - "sec x"] "dx"`
`= 2 int "cos x" "dx" - int "sec"("x") "dx"`
= 2 sin(x) - ln |sec (x) + tan (x)| + C
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