Optimal. Leaf size=17 \[ \frac {5}{16} \left (x^4-3 x^2\right )^{8/5} \]
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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 = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1588} \[ \frac {5}{16} \left (x^4-3 x^2\right )^{8/5} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \left (-3 x+2 x^3\right ) \left (-3 x^2+x^4\right )^{3/5} \, dx &=\frac {5}{16} \left (-3 x^2+x^4\right )^{8/5}\\ \end {align*}
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Mathematica [C] time = 0.06, size = 75, normalized size = 4.41 \[ \frac {5 \left (x^2 \left (x^2-3\right )\right )^{3/5} \left (16 x^4 \, _2F_1\left (-\frac {3}{5},\frac {13}{5};\frac {18}{5};\frac {x^2}{3}\right )-39 x^2 \, _2F_1\left (-\frac {3}{5},\frac {8}{5};\frac {13}{5};\frac {x^2}{3}\right )\right )}{208 \left (1-\frac {x^2}{3}\right )^{3/5}} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 17, normalized size = 1.00 \[ \frac {5}{16} \left (x^4-3 x^2\right )^{8/5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 13, normalized size = 0.76 \[ \frac {5}{16} \, {\left (x^{4} - 3 \, x^{2}\right )}^{\frac {8}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.63, size = 13, normalized size = 0.76 \[ \frac {5}{16} \, {\left (x^{4} - 3 \, x^{2}\right )}^{\frac {8}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.31, size = 14, normalized size = 0.82
method | result | size |
default | \(\frac {5 \left (x^{4}-3 x^{2}\right )^{\frac {8}{5}}}{16}\) | \(14\) |
gosper | \(\frac {5 \left (x^{4}-3 x^{2}\right )^{\frac {3}{5}} x^{2} \left (x^{2}-3\right )}{16}\) | \(22\) |
trager | \(\frac {5 \left (x^{4}-3 x^{2}\right )^{\frac {3}{5}} x^{2} \left (x^{2}-3\right )}{16}\) | \(22\) |
risch | \(\frac {5 x^{2} \left (x^{2} \left (x^{2}-3\right )\right )^{\frac {3}{5}} \left (x^{2}-3\right )}{16}\) | \(22\) |
meijerg | \(\frac {5 \,3^{\frac {3}{5}} \mathrm {signum}\left (-1+\frac {x^{2}}{3}\right )^{\frac {3}{5}} x^{\frac {26}{5}} \hypergeom \left (\left [-\frac {3}{5}, \frac {13}{5}\right ], \left [\frac {18}{5}\right ], \frac {x^{2}}{3}\right )}{13 \left (-\mathrm {signum}\left (-1+\frac {x^{2}}{3}\right )\right )^{\frac {3}{5}}}-\frac {15 \,3^{\frac {3}{5}} \mathrm {signum}\left (-1+\frac {x^{2}}{3}\right )^{\frac {3}{5}} x^{\frac {16}{5}} \hypergeom \left (\left [-\frac {3}{5}, \frac {8}{5}\right ], \left [\frac {13}{5}\right ], \frac {x^{2}}{3}\right )}{16 \left (-\mathrm {signum}\left (-1+\frac {x^{2}}{3}\right )\right )^{\frac {3}{5}}}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 13, normalized size = 0.76 \[ \frac {5}{16} \, {\left (x^{4} - 3 \, x^{2}\right )}^{\frac {8}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 21, normalized size = 1.24 \[ \frac {5\,x^2\,\left (x^2-3\right )\,{\left (x^4-3\,x^2\right )}^{3/5}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.31, size = 36, normalized size = 2.12 \[ \frac {5 x^{4} \left (x^{4} - 3 x^{2}\right )^{\frac {3}{5}}}{16} - \frac {15 x^{2} \left (x^{4} - 3 x^{2}\right )^{\frac {3}{5}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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