Function Expression :
\[f(x)=ln(\frac{x-2}{\sqrt{x+5}} ) \]Domain
\[\left]2, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\sqrt{x + 5} \left(- \frac{x - 2}{2 \left(x + 5\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x + 5}}\right)}{x - 2} \]\[f^{\,\prime}(x)=\frac{x + 12}{2 \left(x - 2\right) \left(x + 5\right)} \]
\[ \]
Integral
\[F(x) = x \log{\left(\frac{x}{\sqrt{x + 5}} - \frac{2}{\sqrt{x + 5}} \right)} - \frac{x}{2} - \frac{7 \log{\left(x + 5 \right)}}{2} - 2 \log{\left(\frac{x}{\sqrt{x + 5}} - \frac{2}{\sqrt{x + 5}} \right)} \]Sign Table
Variation Table
Plot
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