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 = {1588} \[ \frac {4}{15} \left (6 x-x^3\right )^{5/4} \]
Antiderivative was successfully verified.
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Rule 1588
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] time = 0.05, size = 72, normalized size = 4.24 \[ -\frac {4 \sqrt [4]{-x \left (x^2-6\right )} \left (5 x^3 \, _2F_1\left (-\frac {1}{4},\frac {13}{8};\frac {21}{8};\frac {x^2}{6}\right )-26 x \, _2F_1\left (-\frac {1}{4},\frac {5}{8};\frac {13}{8};\frac {x^2}{6}\right )\right )}{65 \sqrt [4]{1-\frac {x^2}{6}}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 20, normalized size = 1.18 \[ -\frac {4}{15} \, {\left (x^{3} - 6 \, x\right )} {\left (-x^{3} + 6 \, x\right )}^{\frac {1}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 13, normalized size = 0.76 \[ \frac {4}{15} \, {\left (-x^{3} + 6 \, x\right )}^{\frac {5}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 1.18 \[ -\frac {4 \left (-x^{3}+6 x \right )^{\frac {1}{4}} \left (x^{2}-6\right ) x}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 13, normalized size = 0.76 \[ \frac {4}{15} \, {\left (-x^{3} + 6 \, x\right )}^{\frac {5}{4}} \]
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 \[ -\frac {4\,x\,\left (x^2-6\right )\,{\left (6\,x-x^3\right )}^{1/4}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.27, size = 31, normalized size = 1.82 \[ - \frac {4 x^{3} \sqrt [4]{- x^{3} + 6 x}}{15} + \frac {8 x \sqrt [4]{- x^{3} + 6 x}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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