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

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

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

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

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

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

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

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

(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4) (ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)

int_(0)^(pi//2)sin^(4)xcos^(5)x dx=

Prove that : int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x)dx hence evaluate : int_(0)^(pi//2) (sin x)/(sin x + cos x) dx