Possibly the strangest calculus problem? (Part 2)

Calculus Level 5

01x21x2x+1dx \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 abcdln3\dfrac{a}{b}-\dfrac{c}{d}\ln3 where a,b,ca,b,c and dd are positive integers with gcd(a,b)=gcd(c,d)=1\gcd(a,b) = \gcd(c,d) = 1. Find a+b+c+da+b+c+d.

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