Optimal. Leaf size=27 \[ -\frac {51}{16} (3-2 x)^{4/3}+\frac {3}{28} (3-2 x)^{7/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} \frac {3}{28} (3-2 x)^{7/3}-\frac {51}{16} (3-2 x)^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \sqrt [3]{3-2 x} (7+x) \, dx &=\int \left (\frac {17}{2} \sqrt [3]{3-2 x}-\frac {1}{2} (3-2 x)^{4/3}\right ) \, dx\\ &=-\frac {51}{16} (3-2 x)^{4/3}+\frac {3}{28} (3-2 x)^{7/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -\frac {3}{112} (3-2 x)^{4/3} (107+8 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 20, normalized size = 0.74
method | result | size |
gosper | \(-\frac {3 \left (8 x +107\right ) \left (3-2 x \right )^{\frac {4}{3}}}{112}\) | \(15\) |
trager | \(\left (\frac {3}{7} x^{2}+\frac {285}{56} x -\frac {963}{112}\right ) \left (3-2 x \right )^{\frac {1}{3}}\) | \(19\) |
derivativedivides | \(-\frac {51 \left (3-2 x \right )^{\frac {4}{3}}}{16}+\frac {3 \left (3-2 x \right )^{\frac {7}{3}}}{28}\) | \(20\) |
default | \(-\frac {51 \left (3-2 x \right )^{\frac {4}{3}}}{16}+\frac {3 \left (3-2 x \right )^{\frac {7}{3}}}{28}\) | \(20\) |
risch | \(-\frac {3 \left (16 x^{2}+190 x -321\right ) \left (2 x -3\right )}{112 \left (3-2 x \right )^{\frac {2}{3}}}\) | \(25\) |
meijerg | \(7 \,3^{\frac {1}{3}} x \hypergeom \left (\left [-\frac {1}{3}, 1\right ], \left [2\right ], \frac {2 x}{3}\right )+\frac {3^{\frac {1}{3}} x^{2} \hypergeom \left (\left [-\frac {1}{3}, 2\right ], \left [3\right ], \frac {2 x}{3}\right )}{2}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.70 \begin {gather*} \frac {3}{28} \, {\left (-2 \, x + 3\right )}^{\frac {7}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.78, size = 19, normalized size = 0.70 \begin {gather*} \frac {3}{112} \, {\left (16 \, x^{2} + 190 \, x - 321\right )} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] Result contains complex when optimal does not.
time = 0.52, size = 112, normalized size = 4.15 \begin {gather*} \begin {cases} \frac {3 \left (x + 7\right )^{2} \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{7} - \frac {51 \left (x + 7\right ) \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{56} - \frac {2601 \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{112} & \text {for}\: \left |{x + 7}\right | > \frac {17}{2} \\\frac {3 \sqrt [3]{3 - 2 x} \left (x + 7\right )^{2}}{7} - \frac {51 \sqrt [3]{3 - 2 x} \left (x + 7\right )}{56} - \frac {2601 \sqrt [3]{3 - 2 x}}{112} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.23, size = 26, normalized size = 0.96 \begin {gather*} \frac {3}{28} \, {\left (2 \, x - 3\right )}^{2} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.26, size = 14, normalized size = 0.52 \begin {gather*} -\frac {3\,{\left (3-2\,x\right )}^{4/3}\,\left (8\,x+107\right )}{112} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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