Optimal. Leaf size=13 \[ \frac{\sqrt{x^6+2}}{3} \]
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Rubi [A] time = 0.0026282, antiderivative size = 13, 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} \[ \frac{\sqrt{x^6+2}}{3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^5}{\sqrt{2+x^6}} \, dx &=\frac{\sqrt{2+x^6}}{3}\\ \end{align*}
Mathematica [A] time = 0.0018357, size = 13, normalized size = 1. \[ \frac{\sqrt{x^6+2}}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{3}\sqrt{{x}^{6}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.990974, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44953, size = 26, normalized size = 2. \begin{align*} \frac{1}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.252104, size = 8, normalized size = 0.62 \begin{align*} \frac{\sqrt{x^{6} + 2}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16945, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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