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

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

int_(0)^(pi)(cos x)/(1-sin^(m)x)dx

3. int_(0)^( pi/2)( sin2 x)/(1+cos^(2)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

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

int_(0)^( pi)( sin x*cos^(3)x)dx

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

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

int_(0)^(pi//6) (sin x) /(cos^(3)x) dx is

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