`int_0^pi sin^4x cos^4x dx`

int_0^(pi/2) sin^4x/(sin^4x+cos^4x) dx=

int_(0)^(pi)sin 5 x cos 4x dx=

int_(0)^( pi)x(sin^(4)x cos^(4)x)dx

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx

Evaluate: int_0^(pi//2)(xsinx cos\ x)/(sin^4x+cos^4x)dx