Function Expression :
\[f(x)=2x^2+3x\sqrt{x} \]Domain
\[\left[0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{9 \sqrt{x}}{2} + 4 x \]\[f^{\,\prime}(x)=\frac{9 \sqrt{x} + 8 x}{2} \]
Integral
\[F(x) = \frac{2 x^{3}}{3} + 3 \left(\begin{cases} \frac{2 x^{\frac{5}{2}}}{5} & \text{for}\: \left|{x}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{7}{2} \\\frac{5}{2} & 0 \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{7}{2}, 1 & \\ & \frac{5}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right) \]Sign Table
Variation Table
Plot
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