Optimal. Leaf size=13 \[ \frac {3}{8} \left (x^4+1\right )^{2/3} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \begin {gather*} \frac {3}{8} \left (x^4+1\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^3}{\sqrt [3]{1+x^4}} \, dx &=\frac {3}{8} \left (1+x^4\right )^{2/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{8} \left (x^4+1\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{8} \left (1+x^4\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{4} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.61, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{4} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
derivativedivides | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
default | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
trager | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
risch | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
meijerg | \(\frac {\hypergeom \left (\left [\frac {1}{3}, 1\right ], \relax [2], -x^{4}\right ) x^{4}}{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{4} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 9, normalized size = 0.69 \begin {gather*} \frac {3\,{\left (x^4+1\right )}^{2/3}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 10, normalized size = 0.77 \begin {gather*} \frac {3 \left (x^{4} + 1\right )^{\frac {2}{3}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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