Optimal. Leaf size=13 \[ -1+e^{\frac {4}{3 x^3}} x \]
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Rubi [A] time = 0.04, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2288} \begin {gather*} e^{\frac {4}{3 x^3}} x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {4}{3 x^3}} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 0.85 \begin {gather*} e^{\frac {4}{3 x^3}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 8, normalized size = 0.62 \begin {gather*} x e^{\left (\frac {4}{3 \, x^{3}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 8, normalized size = 0.62 \begin {gather*} x e^{\left (\frac {4}{3 \, x^{3}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 9, normalized size = 0.69
method | result | size |
risch | \(x \,{\mathrm e}^{\frac {4}{3 x^{3}}}\) | \(9\) |
gosper | \(x \,{\mathrm e}^{\frac {4}{3 x^{3}}}\) | \(11\) |
norman | \(x \,{\mathrm e}^{\frac {4}{3 x^{3}}}\) | \(11\) |
meijerg | \(-\frac {4^{\frac {1}{3}} 3^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} \left (-\frac {3 \left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}}+\frac {3 \,3^{\frac {1}{3}} 4^{\frac {2}{3}} x \left (-1\right )^{\frac {2}{3}} {\mathrm e}^{\frac {4}{3 x^{3}}}}{4}+\frac {3 \left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {4}{3 x^{3}}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}}\right )}{9}-\frac {4^{\frac {1}{3}} 3^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} \left (\frac {\left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}}-\frac {\left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {4}{3 x^{3}}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}}\right )}{3}\) | \(121\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 43, normalized size = 3.31 \begin {gather*} \frac {1}{3} \, \left (\frac {4}{3}\right )^{\frac {1}{3}} x \left (-\frac {1}{x^{3}}\right )^{\frac {1}{3}} \Gamma \left (-\frac {1}{3}, -\frac {4}{3 \, x^{3}}\right ) - \frac {\left (\frac {4}{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}, -\frac {4}{3 \, x^{3}}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.20, size = 8, normalized size = 0.62 \begin {gather*} x\,{\mathrm {e}}^{\frac {4}{3\,x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.62 \begin {gather*} x e^{\frac {4}{3 x^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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