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

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

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

" (7.) "int_(0)^((pi)/(2))(sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx

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

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

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

If int_(0)^(pi//2)sin^(4)x cos^(2)x dx=(pi)/(32) , then int_(0)^(pi//2)sin^(2)x cos^(4)x dx=

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

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

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to