# 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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