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Question
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Solution
Let I = `int (1)/(cosx - sqrt(3)sinx).dx`
I = `int ((1)/(2))/(1/2.cosx - sqrt(3)/2sinx).dx`
= `(1)/(2) int (1)/( cos pi/(3). cosx - sin pi/(3).sin x)dx`
= `(1)/(2) int (1)/cos (pi/3 + x).dx`
= `(1)/(2) int sec(x + pi/3).dx`
= `(1)/(2)log|sec(x + pi/3) + tan(x + pi/3)| + c`.
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