Optimal. Leaf size=34 \[ \frac {12}{x \left (\frac {2}{x}+\frac {1}{5} \left (-4-x-\frac {1}{2} \left (7+e^3\right ) x^2\right )\right )} \]
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Rubi [F]
time = 0.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.01, size = 23, normalized size = 0.68 \begin {gather*} -\frac {120}{-20+8 x+2 x^2+\left (7+e^3\right ) x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 1.12, size = 142, normalized size = 4.18
method | result | size |
gosper | \(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\) | \(26\) |
norman | \(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\) | \(26\) |
risch | \(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\) | \(26\) |
default | \(60 \left (\munderset {\textit {\_R} =\RootOf \left (400+\left ({\mathrm e}^{6}+14 \,{\mathrm e}^{3}+49\right ) \textit {\_Z}^{6}+\left (4 \,{\mathrm e}^{3}+28\right ) \textit {\_Z}^{5}+\left (16 \,{\mathrm e}^{3}+116\right ) \textit {\_Z}^{4}+\left (-40 \,{\mathrm e}^{3}-248\right ) \textit {\_Z}^{3}-16 \textit {\_Z}^{2}-320 \textit {\_Z} \right )}{\sum }\frac {\left (8+3 \left (7+{\mathrm e}^{3}\right ) \textit {\_R}^{2}+4 \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{-160+3 \textit {\_R}^{5} {\mathrm e}^{6}+42 \textit {\_R}^{5} {\mathrm e}^{3}+10 \textit {\_R}^{4} {\mathrm e}^{3}+147 \textit {\_R}^{5}+32 \textit {\_R}^{3} {\mathrm e}^{3}+70 \textit {\_R}^{4}-60 \textit {\_R}^{2} {\mathrm e}^{3}+232 \textit {\_R}^{3}-372 \textit {\_R}^{2}-16 \textit {\_R}}\right )\) | \(142\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 22, normalized size = 0.65 \begin {gather*} -\frac {120}{x^{3} {\left (e^{3} + 7\right )} + 2 \, x^{2} + 8 \, x - 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 25, normalized size = 0.74 \begin {gather*} -\frac {120}{x^{3} e^{3} + 7 \, x^{3} + 2 \, x^{2} + 8 \, x - 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.21, size = 20, normalized size = 0.59 \begin {gather*} - \frac {120}{x^{3} \cdot \left (7 + e^{3}\right ) + 2 x^{2} + 8 x - 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 25, normalized size = 0.74 \begin {gather*} -\frac {120}{x^{3} e^{3} + 7 \, x^{3} + 2 \, x^{2} + 8 \, x - 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 22, normalized size = 0.65 \begin {gather*} -\frac {120}{\left ({\mathrm {e}}^3+7\right )\,x^3+2\,x^2+8\,x-20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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