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

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

int_0^(pi/2) (sinx)/(1+Cos^2x)dx

int_(0)^( pi)(x tan x)/(tan x+sec x)*dx=(pi(pi-2))/(2)

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)(x tan x)/(sec x+cos x)dx is (pi^(2))/(4)(b)(pi^(2))/(2)(c)(3 pi^(2))/(2) (d) (pi^(2))/(3)

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

(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx (ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx

int_(0)^((pi)/(3))(x)/(1+sec x)dx

Evaluate (i) int_0^pi (x sin x)/(1+cos^2 x) dx Evaluate (ii) int_0^pi (4x sin x)/(1+ cos^2 x) dx

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