Optimal. Leaf size=27 \[ \frac {3}{28} (3-2 x)^{7/3}-\frac {51}{16} (3-2 x)^{4/3} \]
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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 = {43} \[ \frac {3}{28} (3-2 x)^{7/3}-\frac {51}{16} (3-2 x)^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
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 \[ -\frac {3}{112} (3-2 x)^{4/3} (8 x+107) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 19, normalized size = 0.70 \[ \frac {3}{112} \, {\left (16 \, x^{2} + 190 \, x - 321\right )} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 26, normalized size = 0.96 \[ \frac {3}{28} \, {\left (2 \, x - 3\right )}^{2} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ -\frac {3 \left (8 x +107\right ) \left (-2 x +3\right )^{\frac {4}{3}}}{112} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 19, normalized size = 0.70 \[ \frac {3}{28} \, {\left (-2 \, x + 3\right )}^{\frac {7}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \]
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 \[ -\frac {3\,{\left (3-2\,x\right )}^{4/3}\,\left (8\,x+107\right )}{112} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.09, size = 114, normalized size = 4.22 \[ \begin {cases} \frac {3 \left (x + 7\right )^{2} \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{7} - \frac {51 \left (x + 7\right ) \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{56} - \frac {2601 \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{112} & \text {for}\: \frac {2 \left |{x + 7}\right |}{17} > 1 \\\frac {3 \sqrt [3]{3 - 2 x} \left (x + 7\right )^{2}}{7} - \frac {51 \sqrt [3]{3 - 2 x} \left (x + 7\right )}{56} - \frac {2601 \sqrt [3]{3 - 2 x}}{112} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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