Function Expression :
\[f(x)=2x\sqrt{x}-2+ln x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
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Derivate
\[f^{\,\prime}(x)=3 \sqrt{x} + \frac{1}{x} \]\[f^{\,\prime}(x)=\frac{3 x^{\frac{3}{2}} + 1}{x} \]
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Integral
\[F(x) = x \log{\left(x \right)} - 3 x + 2 \left(\begin{cases} \frac{2 x^{\frac{5}{2}}}{5} & \text{for}\: \left|{x}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{7}{2} \\\frac{5}{2} & 0 \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{7}{2}, 1 & \\ & \frac{5}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right) \]Sign Table
Variation Table
Plot
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