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

int_(0)^(pi//2)(1)/(1+tan^(3)x)dx=

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

int_(0)^( pi/8)(1)/(1+4x^(2))dx=?

int_(0)^( pi/2)(x)/((1-x^(2)))dx

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

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx

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

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

int_(0)^(pi//2)(dx)/((1+cot^(3)x))=(pi)/(4)