int_(0)^( pi/3)(cos x)/(3+4sin x)dx=lc log((3+2sqrt(3))/(3))

If int_(0)^((pi)/(3))(cos x)/(3+4sin x)dx=k log((3+2sqrt(3))/(3)) then k is equal to

int_(0)^(2 pi)(cos x)/(sqrt(4+3sin x))dx

Show that int_(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3))

Show that int_(0)^(pi//2)(cos x)/((1+sin x )(2 + sin x))dx = log (4/3)

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

int_(0)^((pi)/(2))(4-3sin x)/(4+3cos x)dx

int_(0)^((pi)/(4))(sin x)/(cos3x+3cos x)dx

int_(0)^( pi/2)(cos x)/((2+sin x)(1+sin x))dx equals (a)log((2)/(3))(b)log((3)/(2))(c)log((3)/(4))(d)log((4)/(3))