Function Expression :
\[f(x)=\frac{x^2-3x}{x^2+1} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 x \left(x^{2} - 3 x\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 x - 3}{x^{2} + 1} \]\[f^{\,\prime}(x)=\frac{3 x^{2} + 2 x - 3}{x^{4} + 2 x^{2} + 1} \]
\[ \]
Integral
\[F(x) = x - \frac{3 \log{\left(x^{2} + 1 \right)}}{2} - \operatorname{atan}{\left(x \right)} \]Sign Table
Variation Table
Plot
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