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

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

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

Find the mistake of the following evaluation of the integral I=int_(0)^( pi)(dx)/(1+2sin^(2)x)I=int_(0)^( pi)(dx)/(cos^(2)x+3sin^(2)x)=int_(0)^( pi)(sec^(2)xdx)/(1+3tan^(2)x)=(1)/(sqrt(3))[tan^(-1)(sqrt(3)tan x)]_(0)^( pi)=0

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

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

int_(0)^(1)(tan^(-1)x)/(x)dx is equal to a) int_(0)^(pi/2)(sinx)/(x)dx b) int_(0)^(pi/2)(x)/(sinx)dx c) 1/2int_(0)^(pi/2)(sinx)/(x)dx d) 1/2int_(0)^(pi/2)(x)/(sinx)dx

Using integral int_(0)^(-(pi)/(2))ln(sin x)dx=-int_(0)^( pi)ln(sec x)dx=-(pi)/(2)ln2 and int_(0)^((pi)/(2))ln(tan x)dx=0 and int_(0)^((pi)/(4))ln(1+tan x)dx=(pi)/(8)