Integrate terms in AP

Calculus Level 5

If

\[\displaystyle \int_0^1{x^{2016} (x^{2016} + 1008){\left(x^{2016} + 2016\right)}^{1/2016} \ dx} = \frac{a^{1/b}}{c}\]

where \(a,b,c\) are positive integers, \(a\) is not a multiple of perfect \(b\)th power.

Then find \(b + c - a\).

Bonus: Generalize \(\displaystyle \int {x^n (x^n + d) {(x^n + 2d)}^{1/n} \ dx}\).

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