((pi)/(2))/(-(pi)/(2))(dx)/(1+cot^(4)x)

int_(0)^((pi)/(2))(dx)/(1+cot x)

The value of int_(-(pi)/(2))^((pi)/(2))[cot^(-1)x]dx

If I_(n) = int_((pi)/(4))^((pi)/(2)) cot^(n) x dx , prove that I_(n) + I_(n-2) = (1)/(n-1)

int_(0)^(pi/2)(1)/(1+cot^(4)x)dx=

int_((pi)/(4))^((pi)/(2))e^(x)(log sin x+cot x)dx

int_(0)^((pi)/(2)) (1)/(1 + cot x)dx

int_(0)^( pi/2)(dx)/(1+cot x)

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

The value of int_(0)^((pi)/(4))ln cos((pi)/(4)+x)^(cot((pi)/(4)-x))dx is

int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))=int_(0)^((pi)/(2))(dx)/(1+sqrt(cot x))=(pi)/(4)