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