Optimal. Leaf size=17 \[ \frac {4}{15} \left (6 x-x^3\right )^{5/4} \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1602}
\begin {gather*} \frac {4}{15} \left (6 x-x^3\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 1602
Rubi steps
\begin {align*} \int \left (2-x^2\right ) \sqrt [4]{6 x-x^3} \, dx &=\frac {4}{15} \left (6 x-x^3\right )^{5/4}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 5 vs. order 2 in
optimal.
time = 10.04, size = 72, normalized size = 4.24 \begin {gather*} -\frac {4 \sqrt [4]{-x \left (-6+x^2\right )} \left (-26 x \, _2F_1\left (-\frac {1}{4},\frac {5}{8};\frac {13}{8};\frac {x^2}{6}\right )+5 x^3 \, _2F_1\left (-\frac {1}{4},\frac {13}{8};\frac {21}{8};\frac {x^2}{6}\right )\right )}{65 \sqrt [4]{1-\frac {x^2}{6}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.32, size = 14, normalized size = 0.82
method | result | size |
default | \(\frac {4 \left (-x^{3}+6 x \right )^{\frac {5}{4}}}{15}\) | \(14\) |
risch | \(-\frac {4 \left (-x \left (x^{2}-6\right )\right )^{\frac {1}{4}} x \left (x^{2}-6\right )}{15}\) | \(19\) |
gosper | \(-\frac {4 \left (-x^{3}+6 x \right )^{\frac {1}{4}} x \left (x^{2}-6\right )}{15}\) | \(20\) |
trager | \(-\frac {4 \left (-x^{3}+6 x \right )^{\frac {1}{4}} x \left (x^{2}-6\right )}{15}\) | \(20\) |
meijerg | \(\frac {8 \,6^{\frac {1}{4}} x^{\frac {5}{4}} \hypergeom \left (\left [-\frac {1}{4}, \frac {5}{8}\right ], \left [\frac {13}{8}\right ], \frac {x^{2}}{6}\right )}{5}-\frac {4 \,6^{\frac {1}{4}} x^{\frac {13}{4}} \hypergeom \left (\left [-\frac {1}{4}, \frac {13}{8}\right ], \left [\frac {21}{8}\right ], \frac {x^{2}}{6}\right )}{13}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.76 \begin {gather*} \frac {4}{15} \, {\left (-x^{3} + 6 \, x\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 20, normalized size = 1.18 \begin {gather*} -\frac {4}{15} \, {\left (x^{3} - 6 \, x\right )} {\left (-x^{3} + 6 \, x\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs.
\(2 (12) = 24\).
time = 0.09, size = 31, normalized size = 1.82 \begin {gather*} - \frac {4 x^{3} \sqrt [4]{- x^{3} + 6 x}}{15} + \frac {8 x \sqrt [4]{- x^{3} + 6 x}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.33, size = 13, normalized size = 0.76 \begin {gather*} \frac {4}{15} \, {\left (-x^{3} + 6 \, x\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.16, size = 19, normalized size = 1.12 \begin {gather*} -\frac {4\,x\,\left (x^2-6\right )\,{\left (6\,x-x^3\right )}^{1/4}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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