Question

Evaluate: ${\int }_0^{\pi /3}\frac{\sec x+\tan x}{\tan x}dx$.

Answer 1

${\int }_0^{\pi /3}\frac{\sec x+\tan x}{\tan x}dx{\int }_0^{\pi /3}(1+\sin x)dx{x+\cos x|}_0^{\pi /3}\frac{\pi }{3}+\cos \frac{\pi }{3}-0-\cos 0\frac{\pi }{3}+\frac{1}{2}-1\frac{\pi }{3}-\frac{1}{2}$