Function Expression :
\[f(x)=ln(\frac{x-3}{x+3} ) \]Domain
\[\left]-\infty, -3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-3} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(x + 3\right) \left(- \frac{x - 3}{\left(x + 3\right)^{2}} + \frac{1}{x + 3}\right)}{x - 3} \]\[f^{\,\prime}(x)=\frac{6}{x^{2} - 9} \]
\[ \]
Integral
\[F(x) = x \log{\left(\frac{x}{x + 3} - \frac{3}{x + 3} \right)} - 6 \log{\left(x + 3 \right)} - 3 \log{\left(\frac{x}{x + 3} - \frac{3}{x + 3} \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0238 seconds