Integrate the following functions w. r. t. x : ∫ 1/(cos x - √3 sin x).dx

Question

Integrate the following functions w. r. t. x :

\(\int \frac{1}{cos\,x - \sqrt{3}\,sin\,x}.dx\)

∫ 1/(cos x - √3 sin x).dx

Answer 1

 ∫ 1/(cos x - √3 sin x).dx

Dividing each term by \(\sqrt{1^2 + (-1)^2} = \sqrt{3},\) we get