`int_(0)^( pi)(x sec^(2)x)/(a^(2)+b^(2)tan^(2)x)dx`

Evaluate the following : int_(0)^(pi//4)(sec^(2)x)/(tan^(2)x+4 tanx+1)dx

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

The value of int_(-((pi)/(4))^((1)/(3)))^(((pi)/(4))^((1)/(3)))(x^(2))/((1+sin^(2)x^(3))(1+e^(x)^^7))dxis (a) (1)/(3)tan^(-1)sqrt(2)(b)(1)/(3sqrt(2))tan^(-1)sqrt(2)(c)int_(0)^((pi)/(4))(sec^(2)dx)/(sec^(2)x+tan^(2)x)(d)(1)/(3)int_(0)^((pi)/(4))(sec^(2)dx)/(sec^(2)x+tan^(2)x)

Evaluate: int_(0)^( pi)(pi-x)/(cos^(2)x+b^(2)sin^(2)x)dx

int (tanx sec^(2)x)/((1-tan^(2)x))dx.

int_(0)^(pi//4) (sec^(2)x)/((1+tan x)(2+tan x))dx is equal to

Evaluate: int_(0)^((pi)/(4)) (sec^(2)x)/(3 tan^(2) x+4 tan x+1)dx

int(1)/(sec^(2)x+2tan^(2)x)dx

int_(0)^(oo)(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))dx=(pi)/(2(a+b))

int_(0)^(pi//4)(2sec^(2)x+x^(3)+2)dx