`int_(0)^(2 pi)sin^(4)((x)/(2))*cos^(5)((x)/(2))dx`

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

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

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

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

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

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

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

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

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