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Calculus Level 4

Let \(f:\mathbb R\rightarrow \mathbb R \backslash \{ 3\} \) be a function given by

\[f(x+10)=\frac { f(x)-5 }{ f(x)-3 } \]

then \(\displaystyle \int _{ 10 }^{ 20 }{ f(x)\ dx }\) is equal to?

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