Question

$\int \frac{dx}{\sqrt{3}cosx+sinx}$

Answer 1

$I=\int \frac{dx}{\sqrt{3}cosx+sinx}$

$=\frac{1}{2}\int \frac{dx}{\frac{\sqrt{3}}{2}cosx+sinx.\frac{1}{2}}$

$=\frac{1}{2}\int \frac{dx}{cos(x-\frac{\pi }{6})}$

$=\frac{1}{2}\int sec(x-\frac{\pi }{6})dx$

$=\frac{1}{2}\left[ln\right(sec(x-\frac{\pi }{6})+tan(x-\frac{\pi }{6})]+c$