" i) "int_(0)^((pi)/(2))(sin^((3)/(2))x)/(sin^((3)/(2))x+cos^((3)/(2))x)dx=(pi)/(4)

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

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

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

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

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

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3)x)/(sin^(3)x+cos^(3)x)dx=(pi)/4

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

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