Optimal. Leaf size=17 \[ \frac {16 e^{x^2} \log (2)}{9 \log (-1+x)} \]
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Rubi [B] time = 0.42, antiderivative size = 43, normalized size of antiderivative = 2.53, number of steps used = 3, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {6741, 12, 2288} \begin {gather*} \frac {16 e^{x^2} \log (2) \left (x \log (x-1)-x^2 \log (x-1)\right )}{9 (1-x) x \log ^2(x-1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 e^{x^2} \log (2) \left (1+2 x \log (-1+x)-2 x^2 \log (-1+x)\right )}{(9-9 x) \log ^2(-1+x)} \, dx\\ &=(16 \log (2)) \int \frac {e^{x^2} \left (1+2 x \log (-1+x)-2 x^2 \log (-1+x)\right )}{(9-9 x) \log ^2(-1+x)} \, dx\\ &=\frac {16 e^{x^2} \log (2) \left (x \log (-1+x)-x^2 \log (-1+x)\right )}{9 (1-x) x \log ^2(-1+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {16 e^{x^2} \log (2)}{9 \log (-1+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 14, normalized size = 0.82 \begin {gather*} \frac {16 \, e^{\left (x^{2}\right )} \log \relax (2)}{9 \, \log \left (x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 14, normalized size = 0.82 \begin {gather*} \frac {16 \, e^{\left (x^{2}\right )} \log \relax (2)}{9 \, \log \left (x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.36, size = 15, normalized size = 0.88
method | result | size |
norman | \(\frac {16 \,{\mathrm e}^{x^{2}} \ln \relax (2)}{9 \ln \left (x -1\right )}\) | \(15\) |
risch | \(\frac {16 \,{\mathrm e}^{x^{2}} \ln \relax (2)}{9 \ln \left (x -1\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 14, normalized size = 0.82 \begin {gather*} \frac {16 \, e^{\left (x^{2}\right )} \log \relax (2)}{9 \, \log \left (x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.46, size = 14, normalized size = 0.82 \begin {gather*} \frac {16\,{\mathrm {e}}^{x^2}\,\ln \relax (2)}{9\,\ln \left (x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 15, normalized size = 0.88 \begin {gather*} \frac {16 e^{x^{2}} \log {\relax (2 )}}{9 \log {\left (x - 1 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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