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

Find the value of int_(0)^(2pi)1/(1+tan^(4)x)dx

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

Prove that: int_(0)^(pi//2) (1)/(1+tan^(3)x)=(pi)/(4)

Prove that: int_(0)^(pi//2) (1)/(1+tan^(3)x)=(pi)/(4)

The value of the integral I=int_(0)^(pi)(x)/(1+tan^(6)x)dx, (x not equal to (pi)/(2) ) is equal to

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

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

Find the error in steps to evaluate the following integral int_(0)^(pi)(dx)/(1+2 sin ^(2) x )=int _(0)^(pi)(sec^(2)xdx)/(sec^(2)x+2 tan^(2)x)=int_(0)^(pi) (sec^(2)xdx)/(1+3 tan^(2)x) =(1)/(sqrt3)[tan^(-1)(sqrt3 tan x)]_(0)^(pi)=0

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

int_(0)^( pi/4)(dx)/(1-sin x)