Evaluate: `int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx`

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

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

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

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

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

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

Evaluate the following integral: int_0^(pi//2)(xsinxcosx)/(sin^4x+cos^4x)dx

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

Evaluate: int_0^(pi//2)1/(4sin^2x+5cos^2x)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