Possibly the strangest calculus problem? (Part 2)

$\large \int_0^1\frac{x^{21}}{\sqrt{x^2-x+1}}\,dx$

The value of the integral above has a closed-form that can be expressed as $\dfrac{a}{b}-\dfrac{c}{d}\ln3$ where $a,b,c$ and $d$ are positive integers with $\gcd(a,b) = \gcd(c,d) = 1$ . Find $a+b+c+d$ .