Find the mistake of the following evaluation of the integral `I=int_0^pi(dx)/(1+2sin^2x)` `I=int_0^pi(dx)/(cos^2x+3sin^2x)` `=int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]pi0=0`

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

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

int_0^(pi/3) (secxtanx)/(1+sec^2x)dx

Evaluate the following integral: int_0^(pi//2)(cos^2x)/(1+3sin^2x)dx

Evaluate the following integral: int_0^(pi//2)(sin^2x)/((1+cos x)^2)dx

Evaluate the following definite integrals: int_0^(pi//4)(sqrt(1-sin2x))/(sinx+cosx)dx

Evaluate the following integral: int_0^(pi//2)1/(1+tan^3x)dx

Evaluate the following integral: int_0^(pi//2)1/(1+tan^3x)dx