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