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int(0)^( pi/2)(1)/(1+tan x)dx=(pi)/(4)...

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

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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

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

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

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

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

int_(0)^( pi/2)(dx)/(1+tan^(5)x)

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

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

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