Optimal. Leaf size=13 \[ \frac {3}{20} \left (1+x^4\right )^{5/3} \]
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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 = {267}
\begin {gather*} \frac {3}{20} \left (x^4+1\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x^3 \left (1+x^4\right )^{2/3} \, dx &=\frac {3}{20} \left (1+x^4\right )^{5/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{20} \left (1+x^4\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {3 \left (x^{4}+1\right )^{\frac {5}{3}}}{20}\) | \(10\) |
derivativedivides | \(\frac {3 \left (x^{4}+1\right )^{\frac {5}{3}}}{20}\) | \(10\) |
default | \(\frac {3 \left (x^{4}+1\right )^{\frac {5}{3}}}{20}\) | \(10\) |
risch | \(\frac {3 \left (x^{4}+1\right )^{\frac {5}{3}}}{20}\) | \(10\) |
trager | \(\left (\frac {3}{20}+\frac {3 x^{4}}{20}\right ) \left (x^{4}+1\right )^{\frac {2}{3}}\) | \(16\) |
meijerg | \(\frac {x^{4} \hypergeom \left (\left [-\frac {2}{3}, 1\right ], \left [2\right ], -x^{4}\right )}{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{20} \, {\left (x^{4} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{20} \, {\left (x^{4} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 26 vs.
\(2 (10) = 20\).
time = 0.11, size = 26, normalized size = 2.00 \begin {gather*} \frac {3 x^{4} \left (x^{4} + 1\right )^{\frac {2}{3}}}{20} + \frac {3 \left (x^{4} + 1\right )^{\frac {2}{3}}}{20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{20} \, {\left (x^{4} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} \frac {3\,{\left (x^4+1\right )}^{5/3}}{20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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