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" (ah) "int[sqrt(cot x)+sqrt(tan x)]dx" ...

" (ah) "int[sqrt(cot x)+sqrt(tan x)]dx" and "4 pi

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int sqrt(cot x)dx

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

int(sqrt(cot x)-sqrt(tan x))/(1+3sin2x)*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) (sqrt( cot x))/(sqrt(cot x) - sqrt(tan x)) dx is :