Optimal. Leaf size=13 \[ \frac{2}{3} \left (\sqrt{x}+1\right )^3 \]
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Rubi [A] time = 0.0020405, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{2}{3} \left (\sqrt{x}+1\right )^3 \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\left (1+\sqrt{x}\right )^2}{\sqrt{x}} \, dx &=\frac{2}{3} \left (1+\sqrt{x}\right )^3\\ \end{align*}
Mathematica [A] time = 0.0023733, size = 20, normalized size = 1.54 \[ \frac{2 x^{3/2}}{3}+2 x+2 \sqrt{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 15, normalized size = 1.2 \begin{align*}{\frac{2}{3}{x}^{{\frac{3}{2}}}}+2\,x+2\,\sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993555, size = 12, normalized size = 0.92 \begin{align*} \frac{2}{3} \,{\left (\sqrt{x} + 1\right )}^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1896, size = 36, normalized size = 2.77 \begin{align*} \frac{2}{3} \,{\left (x + 3\right )} \sqrt{x} + 2 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.130712, size = 17, normalized size = 1.31 \begin{align*} \frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + 2 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10494, size = 19, normalized size = 1.46 \begin{align*} \frac{2}{3} \, x^{\frac{3}{2}} + 2 \, x + 2 \, \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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