Optimal. Leaf size=21 \[ x-\frac {e^{x^2}}{(3-\log (6)) \log (x)} \]
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Rubi [F] time = 0.38, 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^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{x (-3+\log (6)) \log ^2(x)} \, dx\\ &=\frac {\int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{x \log ^2(x)} \, dx}{-3+\log (6)}\\ &=\frac {\int \left (-3+\log (6)-\frac {e^{x^2}}{x \log ^2(x)}+\frac {2 e^{x^2} x}{\log (x)}\right ) \, dx}{-3+\log (6)}\\ &=x-\frac {2 \int \frac {e^{x^2} x}{\log (x)} \, dx}{3-\log (6)}-\frac {\int \frac {e^{x^2}}{x \log ^2(x)} \, dx}{-3+\log (6)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 18, normalized size = 0.86 \begin {gather*} x+\frac {e^{x^2}}{(-3+\log (6)) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 27, normalized size = 1.29 \begin {gather*} \frac {{\left (x \log \relax (6) - 3 \, x\right )} \log \relax (x) + e^{\left (x^{2}\right )}}{{\left (\log \relax (6) - 3\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 29, normalized size = 1.38 \begin {gather*} \frac {x \log \relax (6) \log \relax (x) - 3 \, x \log \relax (x) + e^{\left (x^{2}\right )}}{\log \relax (6) \log \relax (x) - 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 18, normalized size = 0.86
method | result | size |
default | \(x +\frac {{\mathrm e}^{x^{2}}}{\left (\ln \relax (6)-3\right ) \ln \relax (x )}\) | \(18\) |
risch | \(x +\frac {{\mathrm e}^{x^{2}}}{\left (\ln \relax (2)+\ln \relax (3)-3\right ) \ln \relax (x )}\) | \(20\) |
norman | \(\frac {x \ln \relax (x )+\frac {{\mathrm e}^{x^{2}}}{\ln \relax (6)-3}}{\ln \relax (x )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 28, normalized size = 1.33 \begin {gather*} \frac {x {\left (\log \relax (3) + \log \relax (2) - 3\right )} \log \relax (x) + e^{\left (x^{2}\right )}}{{\left (\log \relax (3) + \log \relax (2) - 3\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.32, size = 17, normalized size = 0.81 \begin {gather*} x+\frac {{\mathrm {e}}^{x^2}}{\ln \relax (x)\,\left (\ln \relax (6)-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 17, normalized size = 0.81 \begin {gather*} x + \frac {e^{x^{2}}}{- 3 \log {\relax (x )} + \log {\relax (6 )} \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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