Optimal. Leaf size=17 \[ \frac{4}{15} \left (6 x-x^3\right )^{5/4} \]
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Rubi [A] time = 0.0087056, antiderivative size = 17, normalized size of antiderivative = 1., 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*}
Mathematica [C] time = 0.045878, 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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Maple [A] time = 0.004, size = 20, normalized size = 1.2 \begin{align*} -{\frac{4\,x \left ({x}^{2}-6 \right ) }{15}\sqrt [4]{-{x}^{3}+6\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09946, size = 18, normalized size = 1.06 \begin{align*} \frac{4}{15} \,{\left (-x^{3} + 6 \, x\right )}^{\frac{5}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42863, size = 51, normalized size = 3. \begin{align*} -\frac{4}{15} \,{\left (x^{3} - 6 \, x\right )}{\left (-x^{3} + 6 \, x\right )}^{\frac{1}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.251987, size = 31, normalized size = 1.82 \begin{align*} - \frac{4 x^{3} \sqrt [4]{- x^{3} + 6 x}}{15} + \frac{8 x \sqrt [4]{- x^{3} + 6 x}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12287, size = 18, normalized size = 1.06 \begin{align*} \frac{4}{15} \,{\left (-x^{3} + 6 \, x\right )}^{\frac{5}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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