Optimal. Leaf size=28 \[ e^{x \left (3 x \left (-x+\frac {\log (x)}{x}\right )-(-1+\log (3 x))^2\right )} \]
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Rubi [A] time = 0.38, antiderivative size = 31, normalized size of antiderivative = 1.11, number of steps used = 1, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6706} \begin {gather*} 3^{2 x} x^{5 x} e^{-3 x^3-x-x \log ^2(3 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3^{2 x} e^{-x-3 x^3-x \log ^2(3 x)} x^{5 x}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 3.30, size = 0, normalized size = 0.00 \begin {gather*} \int e^{-x-3 x^3+3 x \log (x)+2 x \log (3 x)-x \log ^2(3 x)} \left (4-9 x^2+3 \log (x)-\log ^2(3 x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.23, size = 42, normalized size = 1.50 \begin {gather*} e^{\left (-3 \, x^{3} - x \log \relax (3)^{2} - x \log \relax (x)^{2} + 2 \, x \log \relax (3) - {\left (2 \, x \log \relax (3) - 5 \, x\right )} \log \relax (x) - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 31, normalized size = 1.11 \begin {gather*} e^{\left (-3 \, x^{3} - x \log \left (3 \, x\right )^{2} + 2 \, x \log \left (3 \, x\right ) + 3 \, x \log \relax (x) - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 32, normalized size = 1.14
method | result | size |
derivativedivides | \({\mathrm e}^{-x \ln \left (3 x \right )^{2}+2 x \ln \left (3 x \right )+3 x \ln \relax (x )-3 x^{3}-x}\) | \(32\) |
default | \({\mathrm e}^{-x \ln \left (3 x \right )^{2}+2 x \ln \left (3 x \right )+3 x \ln \relax (x )-3 x^{3}-x}\) | \(32\) |
risch | \(x^{3 x} x^{-2 x \ln \relax (3)} x^{2 x} 9^{x} {\mathrm e}^{-x \left (\ln \relax (x )^{2}+\ln \relax (3)^{2}+3 x^{2}+1\right )}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 31, normalized size = 1.11 \begin {gather*} e^{\left (-3 \, x^{3} - x \log \left (3 \, x\right )^{2} + 2 \, x \log \left (3 \, x\right ) + 3 \, x \log \relax (x) - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.80, size = 41, normalized size = 1.46 \begin {gather*} 9^x\,x^{5\,x-2\,x\,\ln \relax (3)}\,{\mathrm {e}}^{-x\,{\ln \relax (3)}^2}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 34, normalized size = 1.21 \begin {gather*} e^{- 3 x^{3} - x \left (\log {\relax (x )} + \log {\relax (3 )}\right )^{2} + 2 x \left (\log {\relax (x )} + \log {\relax (3 )}\right ) + 3 x \log {\relax (x )} - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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