Recursive Integration

Calculus Level 3

I integrated an integer \(n\) with respect to a variable \(x\) from \(1\) to \(n\), and had a result of \(c\). I then integrated \(c\) with respect again to \(x\) from \(1\) to \(c\) and had a result of \(c_2\). Then I integrated \(c_2\) with respect again to \(x\) from \(1\) to \(c_2\) and had a result of \(c_3\). If \(c_3 = n\), and \(n\) is a nonzero integer greater than 1, then the value of

\( \huge \int^{n}_{1} nx^{n} dx \)

can be expressed in the form \(\frac {a}{b} \) where \(a\) and \(b\) are coprime positive integers. Determine \(a+b\).

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