Function Expression :
\[f(x)=\frac{1}{x^2-2x+3} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 - 2 x}{\left(x^{2} - 2 x + 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \cdot \left(1 - x\right)}{\left(x^{2} - 2 x + 3\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} - \frac{\sqrt{2}}{2} \right)}}{2} \]Sign Table
Variation Table
Plot
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