Question

Evaluate the following integrals: 

`int "sec x"/"sec 2x" "dx"`

Answer 1

\[I = \int\frac{\sec   x}{\sec   2x}dx\]

`"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