Function Expression :
\[f(x)=ln\frac{2x+1}{x-3} \]Domain
\[\left]-\infty, - \frac{1}{2}\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \log{\left(2 \right)} \]\[\lim_{x \overset{<}{\rightarrow- \frac{1}{2}} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \log{\left(2 \right)} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(x - 3\right) \left(\frac{2}{x - 3} - \frac{2 x + 1}{\left(x - 3\right)^{2}}\right)}{2 x + 1} \]\[f^{\,\prime}(x)=\frac{7}{- 2 x^{2} + 5 x + 3} \]
\[ \]
Integral
\[F(x) = x \log{\left(\frac{2 x}{x - 3} + \frac{1}{x - 3} \right)} + \frac{7 \log{\left(2 x + 1 \right)}}{2} - 3 \log{\left(\frac{2 x}{x - 3} + \frac{1}{x - 3} \right)} \]Sign Table
Variation Table
Plot
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