Function Expression :
\[f(x)=\frac{2x-4}{x+3}+ln(x-5 ) \]Domain
\[\left]5, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow5} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2}{x + 3} - \frac{2 x - 4}{\left(x + 3\right)^{2}} + \frac{1}{x - 5} \]\[f^{\,\prime}(x)=\frac{x^{2} + 16 x - 41}{x^{3} + x^{2} - 21 x - 45} \]
\[ \]
Integral
\[F(x) = x \log{\left(x - 5 \right)} + x - 5 \log{\left(x - 5 \right)} - 10 \log{\left(x + 3 \right)} \]Sign Table
Variation Table
Plot
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