Optimal. Leaf size=15 \[ \frac{1}{12} \left (4 x^2+9\right )^{3/2} \]
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Rubi [A] time = 0.0021563, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{1}{12} \left (4 x^2+9\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \sqrt{9+4 x^2} \, dx &=\frac{1}{12} \left (9+4 x^2\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0018369, size = 15, normalized size = 1. \[ \frac{1}{12} \left (4 x^2+9\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 12, normalized size = 0.8 \begin{align*}{\frac{1}{12} \left ( 4\,{x}^{2}+9 \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.22952, size = 15, normalized size = 1. \begin{align*} \frac{1}{12} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49535, size = 32, normalized size = 2.13 \begin{align*} \frac{1}{12} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.184337, size = 27, normalized size = 1.8 \begin{align*} \frac{x^{2} \sqrt{4 x^{2} + 9}}{3} + \frac{3 \sqrt{4 x^{2} + 9}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.55571, size = 15, normalized size = 1. \begin{align*} \frac{1}{12} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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