`int_(0)^( pi)sin^(3)x(1-cos x)^(2)dx`

int_(0)^( pi)(x sin^(3)x)/(1+cos^(2)x)dx

int_(0)^( pi)sin^(3)x(1+2cos x)(1+cos x)^(2)dx

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

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

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

int_(0)^( pi/2)(sin x)/(1+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=

" (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^(2)x)/(sin^(3)x+cos^(3)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