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

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

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

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

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

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

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

If I_(1)=int_(0)^(pi//2)(cos^(2)x)/(1+cos^(2)x)dx,I_(2)=int_(0)^(pi//2)(sin^(2)x)/(1+sin^(2)x)dx , I_(3)=int_(0)^(pi//2)(1+2cos^(2)x.sin^(2)x)/(4+2cos^(2)xsin^(2)x)dx , then