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

int_(0)^(pi/2)(dx)/(1+sqrt(cotx))

Evaluate (i) int_(0)^(pi//2)(d x)/(1+sqrt(tan x)) (ii) int_(0)^(pi//2) log (tan x ) d x (iii) int_(0)^(pi//4) log (1+tan x ) d x (iv) int_(0)^(pi//2)(sin x- cos x)/(1+ sin x cos x)d x

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)

int_(0)^(pi//2)(dx)/(1+e^(sqrt(2)cos(x+(pi)/(4)))) is equal to

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)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

int_(0)^( pi/4)tan^(3)dx

Prove that : int_(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |(sqrt(2)+1)/(sqrt(2)-1)|

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