Function Expression :
\[f(x)=ln(\frac{2x+3}{x-2} ) \]Domain
\[\left]-\infty, - \frac{3}{2}\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \log{\left(2 \right)} \]\[\lim_{x \overset{<}{\rightarrow- \frac{3}{2}} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \log{\left(2 \right)} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(x - 2\right) \left(\frac{2}{x - 2} - \frac{2 x + 3}{\left(x - 2\right)^{2}}\right)}{2 x + 3} \]\[f^{\,\prime}(x)=\frac{7}{- 2 x^{2} + x + 6} \]
\[ \]
Integral
\[F(x) = x \log{\left(\frac{2 x}{x - 2} + \frac{3}{x - 2} \right)} + \frac{7 \log{\left(2 x + 3 \right)}}{2} - 2 \log{\left(\frac{2 x}{x - 2} + \frac{3}{x - 2} \right)} \]Sign Table
Variation Table
Plot
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