`∫ dx/(Cos^2x Sin^2x`

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

(i) int 1/(4sin^2x+5cos^2x) dx (ii) int (dx)/(cos^2 x+2 sin^2x)

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

int(dx)/(cos^(2)x-sin^(2)x)

int(dx)/(cos^(2)x+sin2x)

int (dx)/((cos ^(2)x-3sin^(2)x))=?

int_(0)^(pi)(x dx)/(4 cos^(2)x+9sin^(2)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