Integrand size = 42, antiderivative size = 28 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=-81+e^3+3 \left (-2+\frac {4 e^{-1/x} (x-\log (3))}{\log (x)}\right ) \]
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Time = 0.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6873, 12, 2326} \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {12 e^{-1/x} (x \log (x)-\log (3) \log (x))}{\log ^2(x)} \]
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Rule 12
Rule 2326
Rule 6873
Rubi steps \begin{align*} \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{align*}
Time = 0.20 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {12 e^{-1/x} (x-\log (3))}{\log (x)} \]
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Time = 0.41 (sec) , antiderivative size = 19, normalized size of antiderivative = 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 | \(\frac {\left (12 x^{2}-12 x \ln \left (3\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x \ln \left (x \right )}\) | \(26\) |
parallelrisch | \(-\frac {\left (12 x \ln \left (3\right )-12 x^{2}\right ) {\mathrm e}^{-\frac {1}{x}}}{x \ln \left (x \right )}\) | \(27\) |
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Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.64 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {12 \, {\left (x - \log \left (3\right )\right )} e^{\left (-\frac {1}{x}\right )}}{\log \left (x\right )} \]
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Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.54 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {\left (12 x - 12 \log {\left (3 \right )}\right ) e^{- \frac {1}{x}}}{\log {\left (x \right )}} \]
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\[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\int { -\frac {12 \, {\left (x^{2} - x \log \left (3\right ) - {\left (x^{2} + x - \log \left (3\right )\right )} \log \left (x\right )\right )} e^{\left (-\frac {1}{x}\right )}}{x^{2} \log \left (x\right )^{2}} \,d x } \]
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Time = 0.28 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {12 \, {\left (x e^{\left (-\frac {1}{x}\right )} - e^{\left (-\frac {1}{x}\right )} \log \left (3\right )\right )}}{\log \left (x\right )} \]
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Time = 10.83 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.64 \[ \int \frac {e^{-1/x} \left (-12 x^2+12 x \log (3)+\left (12 x+12 x^2-12 \log (3)\right ) \log (x)\right )}{x^2 \log ^2(x)} \, dx=\frac {12\,{\mathrm {e}}^{-\frac {1}{x}}\,\left (x-\ln \left (3\right )\right )}{\ln \left (x\right )} \]
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