Integration of (2+sqrt x)/(x+sqrt x+ 1)^2

apply eulers subsitution

Using x=u²

dx=2u.du

so its:

integration of (2+u)/(u²+u+1).dx

now, the numerator is derivative of denominator so its:

u² * log(u²+u+1)

because

intergation of f''(x)/f(x) = log[f(x)]