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

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

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

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

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

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

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

STATEMENT-1 : int_(0)^((pi)/(2))(xsinxcosx)/(sin^(4)x+cos^(4)x)dx=(pi^(2))/(32) and STATEMENT-2 : int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

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

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

Prove that : int_(0)^(pi//2) (x sin x cos x)/(sin^(4) x+ cos^(4)x)dx =(pi)/(16)