Optimal. Leaf size=13 \[ \frac {1}{5} \left (1+x^3\right )^{5/3} \]
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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 {1}{5} \left (x^3+1\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x^2 \left (1+x^3\right )^{2/3} \, dx &=\frac {1}{5} \left (1+x^3\right )^{5/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{5} \left (1+x^3\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 |
derivativedivides | \(\frac {\left (x^{3}+1\right )^{\frac {5}{3}}}{5}\) | \(10\) |
default | \(\frac {\left (x^{3}+1\right )^{\frac {5}{3}}}{5}\) | \(10\) |
risch | \(\frac {\left (x^{3}+1\right )^{\frac {5}{3}}}{5}\) | \(10\) |
trager | \(\left (\frac {1}{5}+\frac {x^{3}}{5}\right ) \left (x^{3}+1\right )^{\frac {2}{3}}\) | \(16\) |
meijerg | \(\frac {x^{3} \hypergeom \left (\left [-\frac {2}{3}, 1\right ], \left [2\right ], -x^{3}\right )}{3}\) | \(17\) |
gosper | \(\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (x^{3}+1\right )^{\frac {2}{3}}}{5}\) | \(21\) |
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 {1}{5} \, {\left (x^{3} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{5} \, {\left (x^{3} + 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. 22 vs.
\(2 (8) = 16\).
time = 0.09, size = 22, normalized size = 1.69 \begin {gather*} \frac {x^{3} \left (x^{3} + 1\right )^{\frac {2}{3}}}{5} + \frac {\left (x^{3} + 1\right )^{\frac {2}{3}}}{5} \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 {1}{5} \, {\left (x^{3} + 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 {{\left (x^3+1\right )}^{5/3}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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