Optimal. Leaf size=21 \[ \frac {2 x \left (11-e^{-x^2} x^x\right )}{\log (x)} \]
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Rubi [A] time = 0.57, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 9, number of rules used = 6, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.109, Rules used = {6688, 6742, 2360, 2297, 2298, 2288} \begin {gather*} \frac {22 x}{\log (x)}-\frac {2 e^{-x^2} x^{x+1}}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 2297
Rule 2298
Rule 2360
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-22+22 \log (x)-2 e^{-x^2} x^x \left (-1+\left (1+x-2 x^2\right ) \log (x)+x \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=\int \left (\frac {22 (-1+\log (x))}{\log ^2(x)}-\frac {2 e^{-x^2} x^x \left (-1+\log (x)+x \log (x)-2 x^2 \log (x)+x \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-x^2} x^x \left (-1+\log (x)+x \log (x)-2 x^2 \log (x)+x \log ^2(x)\right )}{\log ^2(x)} \, dx\right )+22 \int \frac {-1+\log (x)}{\log ^2(x)} \, dx\\ &=-\frac {2 e^{-x^2} x^{1+x}}{\log (x)}+22 \int \left (-\frac {1}{\log ^2(x)}+\frac {1}{\log (x)}\right ) \, dx\\ &=-\frac {2 e^{-x^2} x^{1+x}}{\log (x)}-22 \int \frac {1}{\log ^2(x)} \, dx+22 \int \frac {1}{\log (x)} \, dx\\ &=\frac {22 x}{\log (x)}-\frac {2 e^{-x^2} x^{1+x}}{\log (x)}+22 \text {li}(x)-22 \int \frac {1}{\log (x)} \, dx\\ &=\frac {22 x}{\log (x)}-\frac {2 e^{-x^2} x^{1+x}}{\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 21, normalized size = 1.00 \begin {gather*} \frac {2 x \left (11-e^{-x^2} x^x\right )}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 25, normalized size = 1.19 \begin {gather*} -\frac {2 \, {\left (x x^{x} - 11 \, x e^{\left (x^{2}\right )}\right )} e^{\left (-x^{2}\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.70, size = 26, normalized size = 1.24 \begin {gather*} -\frac {2 \, x e^{\left (-x^{2} + x \log \relax (x)\right )}}{\log \relax (x)} + \frac {22 \, x}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 25, normalized size = 1.19
method | result | size |
risch | \(\frac {22 x}{\ln \relax (x )}-\frac {2 x \,{\mathrm e}^{-x^{2}} x^{x}}{\ln \relax (x )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 25, normalized size = 1.19 \begin {gather*} -\frac {2 \, {\left (x x^{x} - 11 \, x e^{\left (x^{2}\right )}\right )} e^{\left (-x^{2}\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.33, size = 25, normalized size = 1.19 \begin {gather*} \frac {2\,x\,{\mathrm {e}}^{-x^2}\,\left (11\,{\mathrm {e}}^{x^2}-x^x\right )}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 24, normalized size = 1.14 \begin {gather*} \frac {22 x}{\log {\relax (x )}} - \frac {2 x e^{- x^{2}} e^{x \log {\relax (x )}}}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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