(sqrt(tan x)+sqrt(cot x))dx

int (sqrt(tan x)-sqrt(cot x))/(1+3 sin 2x)dx

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

int_(0)^((pi)/(2))(4sqrt(cot x))/(4sqrt(tan x) + 4sqrt(cot x)) dx

int sqrt(cot x)dx

Show that: int_(0)^(2)sqrt(tan x)+sqrt(cot x)=sqrt(2)pi

The integral int sqrt(cot x)e^(sqrt(sin x))sqrt(cos x)dx equals

int_0^(pi//2) (sqrt( cot x))/(sqrt(cot x) - sqrt(tan x)) dx is :

Evaluate int_(0)^(pi//2) (sqrt(cot x))/(sqrt(cot x) + sqrt(tan x)) dx.