According to the power rule, the integral of $x^n$ is $\frac{1}{n+1}x^{n+1}+C$, where $C$ is the constant of integration.
In this case, we have $(x-5)^6$, so we can apply the power rule with $n=6$. Using the power rule, we get:
$$\int 14(x-5)^6 dx =
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