Optimal. Leaf size=22 \[ \log \left (3 x+\frac {1}{2} e^{18} (10+e)^2 x-\log (x)\right ) \]
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Rubi [A] time = 0.23, antiderivative size = 19, normalized size of antiderivative = 0.86, number of steps used = 3, number of rules used = 3, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6741, 2561, 6684} \begin {gather*} \log \left (\left (6+e^{18} (10+e)^2\right ) x-2 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2561
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2+\left (6+100 e^{18}+20 e^{19}+e^{20}\right ) x}{6 \left (1+\frac {1}{6} e^{18} (10+e)^2\right ) x^2-2 x \log (x)} \, dx\\ &=\int \frac {-2+\left (6+100 e^{18}+20 e^{19}+e^{20}\right ) x}{x \left (6 \left (1+\frac {1}{6} e^{18} (10+e)^2\right ) x-2 \log (x)\right )} \, dx\\ &=\log \left (\left (6+e^{18} (10+e)^2\right ) x-2 \log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 26, normalized size = 1.18 \begin {gather*} \log \left (6 x+100 e^{18} x+20 e^{19} x+e^{20} x-2 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 24, normalized size = 1.09 \begin {gather*} \log \left (-x e^{20} - 20 \, x e^{19} - 100 \, x e^{18} - 6 \, x + 2 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 24, normalized size = 1.09 \begin {gather*} \log \left (-x e^{20} - 20 \, x e^{19} - 100 \, x e^{18} - 6 \, x + 2 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.05
method | result | size |
risch | \(\ln \left (-\frac {x \,{\mathrm e}^{20}}{2}-10 \,{\mathrm e}^{19} x -50 \,{\mathrm e}^{18} x -3 x +\ln \relax (x )\right )\) | \(23\) |
norman | \(\ln \left ({\mathrm e}^{2} {\mathrm e}^{18} x +20 \,{\mathrm e} \,{\mathrm e}^{18} x +100 \,{\mathrm e}^{18} x +6 x -2 \ln \relax (x )\right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 19, normalized size = 0.86 \begin {gather*} \log \left (-\frac {1}{2} \, x {\left (e^{20} + 20 \, e^{19} + 100 \, e^{18} + 6\right )} + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.39, size = 23, normalized size = 1.05 \begin {gather*} \ln \left (6\,x-2\,\ln \relax (x)+100\,x\,{\mathrm {e}}^{18}+20\,x\,{\mathrm {e}}^{19}+x\,{\mathrm {e}}^{20}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 27, normalized size = 1.23 \begin {gather*} \log {\left (- 50 x e^{18} - 10 x e^{19} - \frac {x e^{20}}{2} - 3 x + \log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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