Function Expression :
\[f(x)=\frac{x^2-2+ln x}{x^2} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x + \frac{1}{x}}{x^{2}} - \frac{2 \left(x^{2} + \log{\left(x \right)} - 2\right)}{x^{3}} \]\[f^{\,\prime}(x)=\frac{5 - 2 \log{\left(x \right)}}{x^{3}} \]
\[ \]
Integral
\[F(x) = x - \frac{\log{\left(x \right)}}{x} + \frac{1}{x} \]Sign Table
Variation Table
Plot
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