Optimal. Leaf size=19 \[ 3+e^{\frac {e^{-3-3 x} x}{\log (4 x)}} \]
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Rubi [F] time = 1.37, 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 {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}} (-1+(1-3 x) \log (4 x))}{\log ^2(4 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log ^2(4 x)}+\frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}} (1-3 x)}{\log (4 x)}\right ) \, dx\\ &=-\int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log ^2(4 x)} \, dx+\int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}} (1-3 x)}{\log (4 x)} \, dx\\ &=\int \left (\frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log (4 x)}-\frac {3 e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}} x}{\log (4 x)}\right ) \, dx-\int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log ^2(4 x)} \, dx\\ &=-\left (3 \int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}} x}{\log (4 x)} \, dx\right )-\int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log ^2(4 x)} \, dx+\int \frac {e^{-3-3 x+\frac {e^{-3-3 x} x}{\log (4 x)}}}{\log (4 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.86, size = 17, normalized size = 0.89 \begin {gather*} e^{\frac {e^{-3-3 x} x}{\log (4 x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (e^{\left (-3 \, x + \log \relax (x) - \log \left (2 \, \log \relax (2) + \log \relax (x)\right ) - 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 25, normalized size = 1.32 \begin {gather*} e^{\left (\frac {x}{2 \, e^{\left (3 \, x + 3\right )} \log \relax (2) + e^{\left (3 \, x + 3\right )} \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 19, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{\frac {x \,{\mathrm e}^{-3 x -3}}{\ln \relax (x )+2 \ln \relax (2)}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 25, normalized size = 1.32 \begin {gather*} e^{\left (\frac {x}{2 \, e^{\left (3 \, x + 3\right )} \log \relax (2) + e^{\left (3 \, x + 3\right )} \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.40, size = 15, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-3}}{\ln \left (4\,x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 15, normalized size = 0.79 \begin {gather*} e^{\frac {x e^{- 3 x - 3}}{\log {\left (4 x \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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