`int_(0)^( pi/2)(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)

Evaluate int_(0)^(2pi)(xcos^(2n)x)/(cos^(2n)x+sin^(2n)x)dx

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

int_(0)^(pi/2)(cos^(5)x dx)/(sin^(5)x+cos^(5)x)

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

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

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

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