int(1+2cos x)/((cos x+2)^(2))dx" and "g(0)=0" then "v

Let g(x)=int(1+2cos x)/((cos x+2)^(2))dx and g(0)=0. then the value of 8g((pi)/(2)) is

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

Let u=int_(0)^((pi)/(4))((cos x)/(sin x+cos x))^(2)dx and v=int_(0)^((pi)/(4))((sin x+cos x)/(cos x))^(2)dx Find the value of (v)/(u)

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

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

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

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

If A=int_(0)^( pi)(cos x)/((x+2)^(2))dx, then int_(0)^( pi/2)(sin2x)/(x+1)dx is equal to