Function Expression :
\[f(x)=\frac{2x^2-2x-1}{x^2}+ln x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{x} + \frac{4 x - 2}{x^{2}} - \frac{2 \cdot \left(2 x^{2} - 2 x - 1\right)}{x^{3}} \]\[f^{\,\prime}(x)=\frac{x^{2} + 2 x + 2}{x^{3}} \]
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Integral
\[F(x) = x \log{\left(x \right)} + x - 2 \log{\left(x \right)} + \frac{1}{x} \]Sign Table
Variation Table
Plot
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