Optimal. Leaf size=13 \[ \frac {2}{9} \left (x^3+1\right )^{3/2} \]
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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 {2}{9} \left (x^3+1\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^2 \sqrt {1+x^3} \, dx &=\frac {2}{9} \left (1+x^3\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{9} \left (x^3+1\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{9} \left (1+x^3\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{9} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{9} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} \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 |
derivativedivides | \(\frac {2 \left (x^{3}+1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
default | \(\frac {2 \left (x^{3}+1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
risch | \(\frac {2 \left (x^{3}+1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
trager | \(\left (\frac {2}{9}+\frac {2 x^{3}}{9}\right ) \sqrt {x^{3}+1}\) | \(16\) |
gosper | \(\frac {2 \left (1+x \right ) \left (x^{2}-x +1\right ) \sqrt {x^{3}+1}}{9}\) | \(21\) |
meijerg | \(-\frac {\frac {4 \sqrt {\pi }}{3}-\frac {2 \sqrt {\pi }\, \left (2 x^{3}+2\right ) \sqrt {x^{3}+1}}{3}}{6 \sqrt {\pi }}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{9} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.69 \begin {gather*} \frac {2\,{\left (x^3+1\right )}^{3/2}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 26, normalized size = 2.00 \begin {gather*} \frac {2 x^{3} \sqrt {x^{3} + 1}}{9} + \frac {2 \sqrt {x^{3} + 1}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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