Function Expression :
\[f(x)=\frac{-x^3+5x}{x^2+3} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 x \left(- x^{3} + 5 x\right)}{\left(x^{2} + 3\right)^{2}} + \frac{5 - 3 x^{2}}{x^{2} + 3} \]\[f^{\,\prime}(x)=\frac{- x^{4} - 14 x^{2} + 15}{x^{4} + 6 x^{2} + 9} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + 4 \log{\left(x^{2} + 3 \right)} \]Sign Table
Variation Table
Plot
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