Integrate : `int_(0)^((pi)/(2))(sin^(7/2) x)/(sin^(7/2) x+cos^(7/2) x)dx`

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

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

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

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

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

" (7.) "int_(0)^((pi)/(2))(sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

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

int_(-pi/2)^(pi/2) sin^(7) x dx

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