`int_(0)^(pi/2)(cos^(3/2)x dx)/(sin^(3/2)x+cos^(3/2)x)`

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sin^(3/2)xdx)/(sin^(3/2)x+cos^(3/2)x)

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

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

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

Evaluate: int_(0)^((pi)/(4))(sin^(2)xcos^(2)xdx)/((sin^(3)x+cos^(3)x)^(2))

Evaluate : int_(0)^(pi/4) (sin^2xcos^2xdx)/((sin^3x+cos^3x)^2)

int_(0)^((pi)/(2))(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx

Show that, int_(0)^((pi)/(2))(sin2x dx)/(sin^(4)x+cos^(4)x)=(pi)/(2)

Prove that, int_(0)^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx=pi^(2) .

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