\(\int\dfrac{1}{x-2}dx=ln\left|x-2\right|+C=\left[{}\begin{matrix}ln\left(x-2\right)+C_1;x>2\\ln\left(2-x\right)+C_2;x< 2\end{matrix}\right.\)
\(\left\{{}\begin{matrix}F\left(3\right)=1\\F\left(1\right)=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}ln\left(1\right)+C_1=1\\ln\left(1\right)+C_2=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}C_1=1\\C_2=2\end{matrix}\right.\)
\(\Rightarrow F\left(0\right)+F\left(4\right)=\left(ln2\right)+2+ln\left(2\right)+1=2ln2+3\)
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