Optimal. Leaf size=20 \[ 2 \sqrt{\frac{2}{3}} x^3+\sqrt{6} x \]
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Rubi [A] time = 0.0038428, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {22} \[ 2 \sqrt{\frac{2}{3}} x^3+\sqrt{6} x \]
Antiderivative was successfully verified.
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Rule 22
Rubi steps
\begin{align*} \int \sqrt{2+4 x^2} \sqrt{3+6 x^2} \, dx &=\sqrt{\frac{2}{3}} \int \left (3+6 x^2\right ) \, dx\\ &=\sqrt{6} x+2 \sqrt{\frac{2}{3}} x^3\\ \end{align*}
Mathematica [A] time = 0.0019961, size = 15, normalized size = 0.75 \[ \sqrt{6} \left (\frac{2 x^3}{3}+x\right ) \]
Antiderivative was successfully verified.
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Maple [C] time = 0.001, size = 38, normalized size = 1.9 \begin{align*}{\frac{x \left ( 2\,{x}^{2}+3 \right ) }{6\,{x}^{2}+3}\sqrt{4\,{x}^{2}+2}\sqrt{6\,{x}^{2}+3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{6 \, x^{2} + 3} \sqrt{4 \, x^{2} + 2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.76583, size = 85, normalized size = 4.25 \begin{align*} \frac{{\left (2 \, x^{3} + 3 \, x\right )} \sqrt{6 \, x^{2} + 3} \sqrt{4 \, x^{2} + 2}}{3 \,{\left (2 \, x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 6.09365, size = 17, normalized size = 0.85 \begin{align*} \frac{2 \sqrt{6} x^{3}}{3} + \sqrt{6} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08836, size = 23, normalized size = 1.15 \begin{align*} \frac{1}{3} \, \sqrt{3} \sqrt{2}{\left (2 \, x^{3} + 3 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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