Function Expression :
\[f(x)=\frac{(x\sqrt{x+1}-6 )}{x-3} \]Domain
\[\left[-1, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = \frac{3}{2} \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = \frac{11}{4} \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = \frac{11}{4} \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\frac{x}{2 \sqrt{x + 1}} + \sqrt{x + 1}}{x - 3} - \frac{x \sqrt{x + 1} - 6}{\left(x - 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{x^{2} - 9 x + 12 \sqrt{x + 1} - 6}{2 \sqrt{x + 1} \left(x^{2} - 6 x + 9\right)} \]
\[ \]
Integral
\[F(x) = \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} + 6 \sqrt{x + 1} - 12 \log{\left(\sqrt{x + 1} + 2 \right)} \]Sign Table
Variation Table
Plot
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