Optimal. Leaf size=28 \[ -81+e^3+3 \left (-2+\frac {4 e^{-1/x} (x-\log (3))}{\log (x)}\right ) \]
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Rubi [A]
time = 0.48, antiderivative size = 24, normalized size of antiderivative = 0.86, number of steps
used = 3, number of rules used = 3, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6873, 12, 2326}
\begin {gather*} \frac {12 e^{-1/x} (x \log (x)-\log (3) \log (x))}{\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 e^{-1/x} \left (-x^2+x \log (3)+x \log (x)+x^2 \log (x)-\log (3) \log (x)\right )}{x^2 \log ^2(x)} \, dx\\ &=12 \int \frac {e^{-1/x} \left (-x^2+x \log (3)+x \log (x)+x^2 \log (x)-\log (3) \log (x)\right )}{x^2 \log ^2(x)} \, dx\\ &=\frac {12 e^{-1/x} (x \log (x)-\log (3) \log (x))}{\log ^2(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 19, normalized size = 0.68 \begin {gather*} \frac {12 e^{-1/x} (x-\log (3))}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.18, size = 19, normalized size = 0.68
method | result | size |
risch | \(-\frac {12 \left (\ln \left (3\right )-x \right ) {\mathrm e}^{-\frac {1}{x}}}{\ln \left (x \right )}\) | \(19\) |
derivativedivides | \(\frac {\left (12-\frac {12 \ln \left (3\right )}{x}\right ) x \,{\mathrm e}^{-\frac {1}{x}}}{\ln \left (x \right )}\) | \(22\) |
norman | \(\frac {\left (12 x^{2}-12 x \ln \left (3\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x \ln \left (x \right )}\) | \(26\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 18, normalized size = 0.64 \begin {gather*} \frac {12 \, {\left (x - \log \left (3\right )\right )} e^{\left (-\frac {1}{x}\right )}}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.54 \begin {gather*} \frac {\left (12 x - 12 \log {\left (3 \right )}\right ) e^{- \frac {1}{x}}}{\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 25, normalized size = 0.89 \begin {gather*} \frac {12 \, {\left (x e^{\left (-\frac {1}{x}\right )} - e^{\left (-\frac {1}{x}\right )} \log \left (3\right )\right )}}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.63, size = 18, normalized size = 0.64 \begin {gather*} \frac {12\,{\mathrm {e}}^{-\frac {1}{x}}\,\left (x-\ln \left (3\right )\right )}{\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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