Evaluate the following integrals: ∫1/(√3 sinx +cosx) dx ​

Question

Evaluate the following integrals:

\(\int\frac{1}{\sqrt 3 sinx +cosx}\)dx

Answer 1

Given,

I =  \(\int\frac{1}{\sqrt 3 sinx +cosx}\)dx

Let √3 = r cosθ and 1 = r sinθ

r = \(\sqrt{3+1}\) = 2

And tan θ = 1/√3 → θ = π/6

We know that,