Evaluate the integral $\int \frac{\sec x}{\sqrt{3+\tan x}}dx$ Evaluate the following integral.$$\int \frac{\sec x}{\sqrt{3+\tan x}}dx$$
On putting $t=\tan x$ I am getting $$\int\frac{1}{\sqrt{(t^2+1)(t+3)}}dt$$.
How should i proceed from here.

Mathematica gives this answer:
$$\left(\frac{1}{5}+\frac{3 i}{5}\right) \sqrt{-\frac{3}{10}-\frac{i}{10}} \cos (x) *\\ \sqrt{(1+3 i)-(3-i) \tan (x)} \sqrt{(-3-i) (\tan (x)+i)} F\left(i \sinh ^{-1}\left(\sqrt{-\frac{3}{10}-\frac{i}{10}} \sqrt{\tan
   (x)+3}\right)|\frac{4}{5}-\frac{3 i}{5}\right)$$
