Optimal. Leaf size=15 \[ \frac {3}{4} \left (-x+x^3\right )^{4/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {1602}
\begin {gather*} \frac {3}{4} \left (x^3-x\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1602
Rubi steps
\begin {align*} \int \left (-1+3 x^2\right ) \sqrt [3]{-x+x^3} \, dx &=\frac {3}{4} \left (-x+x^3\right )^{4/3}\\ \end {align*}
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Mathematica [A]
time = 0.75, size = 15, normalized size = 1.00 \begin {gather*} \frac {3}{4} \left (x \left (-1+x^2\right )\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 12, normalized size = 0.80
method | result | size |
derivativedivides | \(\frac {3 \left (x^{3}-x \right )^{\frac {4}{3}}}{4}\) | \(12\) |
default | \(\frac {3 \left (x^{3}-x \right )^{\frac {4}{3}}}{4}\) | \(12\) |
trager | \(\frac {3 x \left (x^{2}-1\right ) \left (x^{3}-x \right )^{\frac {1}{3}}}{4}\) | \(18\) |
risch | \(\frac {3 \left (x \left (x^{2}-1\right )\right )^{\frac {1}{3}} x \left (x^{2}-1\right )}{4}\) | \(18\) |
gosper | \(\frac {3 \left (-1+x \right ) \left (1+x \right ) x \left (x^{3}-x \right )^{\frac {1}{3}}}{4}\) | \(19\) |
meijerg | \(-\frac {3 \mathrm {signum}\left (x^{2}-1\right )^{\frac {1}{3}} x^{\frac {4}{3}} \hypergeom \left (\left [-\frac {1}{3}, \frac {2}{3}\right ], \left [\frac {5}{3}\right ], x^{2}\right )}{4 \left (-\mathrm {signum}\left (x^{2}-1\right )\right )^{\frac {1}{3}}}+\frac {9 \mathrm {signum}\left (x^{2}-1\right )^{\frac {1}{3}} x^{\frac {10}{3}} \hypergeom \left (\left [-\frac {1}{3}, \frac {5}{3}\right ], \left [\frac {8}{3}\right ], x^{2}\right )}{10 \left (-\mathrm {signum}\left (x^{2}-1\right )\right )^{\frac {1}{3}}}\) | \(66\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.73 \begin {gather*} \frac {3}{4} \, {\left (x^{3} - x\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 11, normalized size = 0.73 \begin {gather*} \frac {3}{4} \, {\left (x^{3} - x\right )}^{\frac {4}{3}} \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. 27 vs.
\(2 (10) = 20\).
time = 0.07, size = 27, normalized size = 1.80 \begin {gather*} \frac {3 x^{3} \sqrt [3]{x^{3} - x}}{4} - \frac {3 x \sqrt [3]{x^{3} - x}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.73 \begin {gather*} \frac {3}{4} \, {\left (x^{3} - x\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 11, normalized size = 0.73 \begin {gather*} \frac {3\,{\left (x^3-x\right )}^{4/3}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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