# Repeated indefinite integral

Calculus Level 5

Let

\begin{align*}f(n)&=\displaystyle\underbrace{\iint\cdots\int}_{n\text{ times}} \underbrace{dxdx\cdots dx}_{n\text{ times}}\\ &=\dfrac{x^n}{a_0}+\dfrac{c_1x^{n-1}}{a_1}+\dfrac{c_2x^{n-2}}{a_2}+\cdots +\dfrac{c_n}{a_n}\end{align*}

where $$a_i$$ and $$c_i$$ are constants left over from performing the integration. Let $$g(n)=\displaystyle\sum^n_{i=0}{a_i}$$ where $$a_i$$ are the constants in $$f(n).$$ Find the last three digits of $$g(10).$$

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