Optimal. Leaf size=38 \[ -\frac {3}{10} (1-x)^{10/3}+\frac {12}{7} (1-x)^{7/3}-3 (1-x)^{4/3} \]
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Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} -\frac {3}{10} (1-x)^{10/3}+\frac {12}{7} (1-x)^{7/3}-3 (1-x)^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \sqrt [3]{1-x} (1+x)^2 \, dx &=\int \left (4 \sqrt [3]{1-x}-4 (1-x)^{4/3}+(1-x)^{7/3}\right ) \, dx\\ &=-3 (1-x)^{4/3}+\frac {12}{7} (1-x)^{7/3}-\frac {3}{10} (1-x)^{10/3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.61 \begin {gather*} -\frac {3}{70} (1-x)^{4/3} \left (7 x^2+26 x+37\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 31, normalized size = 0.82 \begin {gather*} -\frac {3}{70} \left (7 (1-x)^2-40 (1-x)+70\right ) (1-x)^{4/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 24, normalized size = 0.63 \begin {gather*} \frac {3}{70} \, {\left (7 \, x^{3} + 19 \, x^{2} + 11 \, x - 37\right )} {\left (-x + 1\right )}^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 38, normalized size = 1.00 \begin {gather*} \frac {3}{10} \, {\left (x - 1\right )}^{3} {\left (-x + 1\right )}^{\frac {1}{3}} + \frac {12}{7} \, {\left (x - 1\right )}^{2} {\left (-x + 1\right )}^{\frac {1}{3}} - 3 \, {\left (-x + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.53 \begin {gather*} -\frac {3 \left (7 x^{2}+26 x +37\right ) \left (-x +1\right )^{\frac {4}{3}}}{70} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 28, normalized size = 0.74 \begin {gather*} -\frac {3}{10} \, {\left (-x + 1\right )}^{\frac {10}{3}} + \frac {12}{7} \, {\left (-x + 1\right )}^{\frac {7}{3}} - 3 \, {\left (-x + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 21, normalized size = 0.55 \begin {gather*} -\frac {3\,{\left (1-x\right )}^{4/3}\,\left (40\,x+7\,{\left (x-1\right )}^2+30\right )}{70} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.52, size = 146, normalized size = 3.84 \begin {gather*} \begin {cases} - \frac {3 \sqrt [3]{x - 1} \left (x + 1\right )^{3} e^{- \frac {2 i \pi }{3}}}{10} + \frac {3 \sqrt [3]{x - 1} \left (x + 1\right )^{2} e^{- \frac {2 i \pi }{3}}}{35} + \frac {9 \sqrt [3]{x - 1} \left (x + 1\right ) e^{- \frac {2 i \pi }{3}}}{35} + \frac {54 \sqrt [3]{x - 1} e^{- \frac {2 i \pi }{3}}}{35} & \text {for}\: \frac {\left |{x + 1}\right |}{2} > 1 \\\frac {3 \sqrt [3]{1 - x} \left (x + 1\right )^{3}}{10} - \frac {3 \sqrt [3]{1 - x} \left (x + 1\right )^{2}}{35} - \frac {9 \sqrt [3]{1 - x} \left (x + 1\right )}{35} - \frac {54 \sqrt [3]{1 - x}}{35} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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