Optimal. Leaf size=17 \[ -\frac{1}{9} \left (a^6-x^6\right )^{3/2} \]
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Rubi [A] time = 0.003434, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {261} \[ -\frac{1}{9} \left (a^6-x^6\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^5 \sqrt{a^6-x^6} \, dx &=-\frac{1}{9} \left (a^6-x^6\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0047003, size = 17, normalized size = 1. \[ -\frac{1}{9} \left (a^6-x^6\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 43, normalized size = 2.5 \begin{align*} -{\frac{ \left ( a-x \right ) \left ( a+x \right ) \left ({a}^{2}+ax+{x}^{2} \right ) \left ({a}^{2}-ax+{x}^{2} \right ) }{9}\sqrt{{a}^{6}-{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993456, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{9} \,{\left (a^{6} - x^{6}\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41476, size = 32, normalized size = 1.88 \begin{align*} -\frac{1}{9} \,{\left (a^{6} - x^{6}\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.323603, size = 29, normalized size = 1.71 \begin{align*} - \frac{a^{6} \sqrt{a^{6} - x^{6}}}{9} + \frac{x^{6} \sqrt{a^{6} - x^{6}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17214, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{9} \,{\left (a^{6} - x^{6}\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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