=(1)/(2)sin(pi tan)_(0)^( pi/2)x*cot xdx=(pi)/(2)log2

int_(0)^(pi//2)x cot x dx=(pi)/(2)(log2)

int_(0)^( pi/2)x sin xdx

int_(0)^( pi/2)log[tan x*cot x]dx

int_(-pi/2)^( pi/2)x*sin xdx

int_(0)^((pi)/(2))x^(2)cos ec^(2)xdx=pi log2

int_(0)^((pi)/(2))x^(2)cos ec^(2)xdx=pi log2

int_(0)^(pi//2) ln (tan x+ cot x)dx=

Prove that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=(pi)/(4)

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2