sqrt(cot sqrt(x))

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

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

If int(sqrt(cot x)-sqrt(tan x))/(sqrt(2)(cos x+sin x)))dx=phi(x),x in(0,(pi)/(2)) and phi((pi)/(4))=(pi)/(2) and maximum value of phi(x) is lambda then [5 lambda] equals (.] GIF )

If int(sqrt(cot x)-sqrt(tan x))/(4+3sin2x)dx=(1)/(2sqrt(2))ln|(f(x)+a)/(f(x)-a)| where 0 < x < (pi)/(2) then find the value of a.

lntegrate the following function with respect to x , (cot sqrt(x))/(2 sqrt(x))

2sqrt(cot(x^(2)))

int sqrt(cot x)dx

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