Function Expression :
\[f(x)=\frac{2x+1}{-x^2+2x-5} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 x - 2\right) \left(2 x + 1\right)}{\left(- x^{2} + 2 x - 5\right)^{2}} + \frac{2}{- x^{2} + 2 x - 5} \]\[f^{\,\prime}(x)=\frac{2 \left(x^{2} + x - 6\right)}{x^{4} - 4 x^{3} + 14 x^{2} - 20 x + 25} \]
\[ \]
Integral
\[F(x) = - \log{\left(x^{2} - 2 x + 5 \right)} - \frac{3 \operatorname{atan}{\left(\frac{x}{2} - \frac{1}{2} \right)}}{2} \]Sign Table
Variation Table
Plot
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