`int_(0)^( pi/2)(sin^(1/4)x)/(sin^(1/4)x+cos^(1/4)x)dx`

The value of int_(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx is

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

int _(-pi)^(pi) (sin^(4)x)/(sin^(2) x + cos^(4) x )dx is equal to

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

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

int_(pi)^((3pi)/2)(sin^(4)x+cos^(4)x)dx

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

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

int(1)/(sin^(2)x-4 cos^(2)x)dx