Function Expression :
\[f(x)=\frac{2x^3+3}{x^2-1} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{6 x^{2}}{x^{2} - 1} - \frac{2 x \left(2 x^{3} + 3\right)}{\left(x^{2} - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 x \left(x^{3} - 3 x - 3\right)}{x^{4} - 2 x^{2} + 1} \]
\[ \]
Integral
\[F(x) = x^{2} + \frac{5 \log{\left(x - 1 \right)}}{2} - \frac{\log{\left(x + 1 \right)}}{2} \]Sign Table
Variation Table
Plot
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