Optimal. Leaf size=28 \[ \frac {e^{-x+\frac {x}{3+3 (4-x) x^2}} x}{\log (3)} \]
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Rubi [F] time = 6.19, 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*} \int \frac {\exp \left (\frac {2 x+12 x^3-3 x^4+\left (-3-12 x^2+3 x^3\right ) \log \left (\frac {x}{\log (3)}\right )}{-3-12 x^2+3 x^3}\right ) \left (3-2 x+24 x^2-34 x^3+56 x^4-72 x^5+27 x^6-3 x^7\right )}{3 x+24 x^3-6 x^4+48 x^5-24 x^6+3 x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \left (3-2 x+24 x^2-34 x^3+56 x^4-72 x^5+27 x^6-3 x^7\right )}{3 \left (1+4 x^2-x^3\right )^2 \log (3)} \, dx\\ &=\frac {\int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \left (3-2 x+24 x^2-34 x^3+56 x^4-72 x^5+27 x^6-3 x^7\right )}{\left (1+4 x^2-x^3\right )^2} \, dx}{3 \log (3)}\\ &=\frac {\int \left (3 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right )-3 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x+\frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \left (4+3 x+16 x^2\right )}{\left (-1-4 x^2+x^3\right )^2}+\frac {2 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) (2+x)}{-1-4 x^2+x^3}\right ) \, dx}{3 \log (3)}\\ &=\frac {\int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \left (4+3 x+16 x^2\right )}{\left (-1-4 x^2+x^3\right )^2} \, dx}{3 \log (3)}+\frac {2 \int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) (2+x)}{-1-4 x^2+x^3} \, dx}{3 \log (3)}+\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \, dx}{\log (3)}-\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x \, dx}{\log (3)}\\ &=\frac {\int \left (\frac {4 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right )}{\left (-1-4 x^2+x^3\right )^2}+\frac {3 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x}{\left (-1-4 x^2+x^3\right )^2}+\frac {16 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x^2}{\left (-1-4 x^2+x^3\right )^2}\right ) \, dx}{3 \log (3)}+\frac {2 \int \left (\frac {2 \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right )}{-1-4 x^2+x^3}+\frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x}{-1-4 x^2+x^3}\right ) \, dx}{3 \log (3)}+\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \, dx}{\log (3)}-\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x \, dx}{\log (3)}\\ &=\frac {2 \int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x}{-1-4 x^2+x^3} \, dx}{3 \log (3)}+\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) \, dx}{\log (3)}-\frac {\int \exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x \, dx}{\log (3)}+\frac {\int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x}{\left (-1-4 x^2+x^3\right )^2} \, dx}{\log (3)}+\frac {4 \int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right )}{\left (-1-4 x^2+x^3\right )^2} \, dx}{3 \log (3)}+\frac {4 \int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right )}{-1-4 x^2+x^3} \, dx}{3 \log (3)}+\frac {16 \int \frac {\exp \left (\frac {x \left (2+12 x^2-3 x^3\right )}{3 \left (-1-4 x^2+x^3\right )}\right ) x^2}{\left (-1-4 x^2+x^3\right )^2} \, dx}{3 \log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 26, normalized size = 0.93 \begin {gather*} \frac {e^{x \left (-1+\frac {1}{3+12 x^2-3 x^3}\right )} x}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 48, normalized size = 1.71 \begin {gather*} e^{\left (-\frac {3 \, x^{4} - 12 \, x^{3} - 3 \, {\left (x^{3} - 4 \, x^{2} - 1\right )} \log \left (\frac {x}{\log \relax (3)}\right ) - 2 \, x}{3 \, {\left (x^{3} - 4 \, x^{2} - 1\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.39, size = 119, normalized size = 4.25 \begin {gather*} e^{\left (-\frac {x^{4}}{x^{3} - 4 \, x^{2} - 1} + \frac {x^{3} \log \left (\frac {x}{\log \relax (3)}\right )}{x^{3} - 4 \, x^{2} - 1} + \frac {4 \, x^{3}}{x^{3} - 4 \, x^{2} - 1} - \frac {4 \, x^{2} \log \left (\frac {x}{\log \relax (3)}\right )}{x^{3} - 4 \, x^{2} - 1} + \frac {2 \, x}{3 \, {\left (x^{3} - 4 \, x^{2} - 1\right )}} - \frac {\log \left (\frac {x}{\log \relax (3)}\right )}{x^{3} - 4 \, x^{2} - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 63, normalized size = 2.25
method | result | size |
gosper | \({\mathrm e}^{\frac {3 \ln \left (\frac {x}{\ln \relax (3)}\right ) x^{3}-3 x^{4}-12 \ln \left (\frac {x}{\ln \relax (3)}\right ) x^{2}+12 x^{3}-3 \ln \left (\frac {x}{\ln \relax (3)}\right )+2 x}{3 x^{3}-12 x^{2}-3}}\) | \(63\) |
risch | \({\mathrm e}^{-\frac {-3 \ln \left (\frac {x}{\ln \relax (3)}\right ) x^{3}+3 x^{4}+12 \ln \left (\frac {x}{\ln \relax (3)}\right ) x^{2}-12 x^{3}+3 \ln \left (\frac {x}{\ln \relax (3)}\right )-2 x}{3 \left (x^{3}-4 x^{2}-1\right )}}\) | \(63\) |
norman | \(\frac {x^{3} {\mathrm e}^{\frac {\left (3 x^{3}-12 x^{2}-3\right ) \ln \left (\frac {x}{\ln \relax (3)}\right )-3 x^{4}+12 x^{3}+2 x}{3 x^{3}-12 x^{2}-3}}-4 x^{2} {\mathrm e}^{\frac {\left (3 x^{3}-12 x^{2}-3\right ) \ln \left (\frac {x}{\ln \relax (3)}\right )-3 x^{4}+12 x^{3}+2 x}{3 x^{3}-12 x^{2}-3}}-{\mathrm e}^{\frac {\left (3 x^{3}-12 x^{2}-3\right ) \ln \left (\frac {x}{\ln \relax (3)}\right )-3 x^{4}+12 x^{3}+2 x}{3 x^{3}-12 x^{2}-3}}}{x^{3}-4 x^{2}-1}\) | \(176\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {1}{3} \, \int \frac {{\left (3 \, x^{7} - 27 \, x^{6} + 72 \, x^{5} - 56 \, x^{4} + 34 \, x^{3} - 24 \, x^{2} + 2 \, x - 3\right )} e^{\left (-\frac {3 \, x^{4} - 12 \, x^{3} - 3 \, {\left (x^{3} - 4 \, x^{2} - 1\right )} \log \left (\frac {x}{\log \relax (3)}\right ) - 2 \, x}{3 \, {\left (x^{3} - 4 \, x^{2} - 1\right )}}\right )}}{x^{7} - 8 \, x^{6} + 16 \, x^{5} - 2 \, x^{4} + 8 \, x^{3} + x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 145, normalized size = 5.18 \begin {gather*} x^{\frac {12\,x^2}{-3\,x^3+12\,x^2+3}-\frac {x^3-1}{-x^3+4\,x^2+1}}\,{\mathrm {e}}^{-\frac {2\,x}{-3\,x^3+12\,x^2+3}}\,{\mathrm {e}}^{\frac {3\,x^4}{-3\,x^3+12\,x^2+3}}\,{\mathrm {e}}^{-\frac {12\,x^3}{-3\,x^3+12\,x^2+3}}\,{\ln \relax (3)}^{\frac {x^3-1}{-x^3+4\,x^2+1}-\frac {12\,x^2}{-3\,x^3+12\,x^2+3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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