NEW FUNCTION

Function Expression :

\[f(x)=-x^2+1-ln x \]

Domain

\[\left]0, \infty\right[ \]

Limits

\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]

Derivate

\[f^{\,\prime}(x)=- 2 x - \frac{1}{x} \]
\[f^{\,\prime}(x)=\frac{- 2 x^{2} - 1}{x} \]

Integral

\[F(x) = - \frac{x^{3}}{3} - x \log{\left(x \right)} + 2 x \]

Sign Table

Variation Table

Plot

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