evaluate: `int_0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx`

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

By using the properties of definite integrals, evaluate the integrals int_0^(pi/2)(sin^(3/2)x dx)/(sin^(3/2)+cos^(3/2)x)

Evaluate int_0^(pi/2) sin^2x dx

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

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

Evaluate: int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

Evaluate : int_(0)^(pi/2)(sin^2x-cos^2x)/(sin^3x+cos^3x)dx

int_0^(pi/2) sin^3x/(sin^3x+cos^3x)dx

The value of int_(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx is

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