Optimal. Leaf size=23 \[ 1+3 \log \left (-5+2 e^x (5-x-\log (3)+\log (x))\right ) \]
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Rubi [F] time = 2.39, 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 \left (6+24 x-6 x^2-6 x \log (3)\right )+6 e^x x \log (x)}{-5 x+e^x \left (10 x-2 x^2-2 x \log (3)\right )+2 e^x x \log (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 {6 e^x \left (-1+x^2-4 x \left (1-\frac {\log (3)}{4}\right )-x \log (x)\right )}{5 x-e^x \left (10 x-2 x^2-2 x \log (3)\right )-2 e^x x \log (x)} \, dx\\ &=6 \int \frac {e^x \left (-1+x^2-4 x \left (1-\frac {\log (3)}{4}\right )-x \log (x)\right )}{5 x-e^x \left (10 x-2 x^2-2 x \log (3)\right )-2 e^x x \log (x)} \, dx\\ &=6 \int \left (\frac {e^x x}{5+2 e^x x-10 e^x \left (1-\frac {\log (3)}{5}\right )-2 e^x \log (x)}+\frac {e^x (-4+\log (3))}{5+2 e^x x-10 e^x \left (1-\frac {\log (3)}{5}\right )-2 e^x \log (x)}+\frac {e^x}{x \left (-5-2 e^x x+10 e^x \left (1-\frac {\log (3)}{5}\right )+2 e^x \log (x)\right )}+\frac {e^x \log (x)}{-5-2 e^x x+10 e^x \left (1-\frac {\log (3)}{5}\right )+2 e^x \log (x)}\right ) \, dx\\ &=6 \int \frac {e^x x}{5+2 e^x x-10 e^x \left (1-\frac {\log (3)}{5}\right )-2 e^x \log (x)} \, dx+6 \int \frac {e^x}{x \left (-5-2 e^x x+10 e^x \left (1-\frac {\log (3)}{5}\right )+2 e^x \log (x)\right )} \, dx+6 \int \frac {e^x \log (x)}{-5-2 e^x x+10 e^x \left (1-\frac {\log (3)}{5}\right )+2 e^x \log (x)} \, dx-(6 (4-\log (3))) \int \frac {e^x}{5+2 e^x x-10 e^x \left (1-\frac {\log (3)}{5}\right )-2 e^x \log (x)} \, dx\\ &=6 \int \frac {e^x x}{5+e^x (-10+2 x+\log (9))-2 e^x \log (x)} \, dx+6 \int \frac {e^x}{x \left (-5-2 e^x x+10 e^x \left (1-\frac {\log (3)}{5}\right )+2 e^x \log (x)\right )} \, dx+6 \int \frac {e^x \log (x)}{-5-2 e^x (-5+x+\log (3))+2 e^x \log (x)} \, dx-(6 (4-\log (3))) \int \frac {e^x}{5+e^x (-10+2 x+\log (9))-2 e^x \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 1.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^x \left (6+24 x-6 x^2-6 x \log (3)\right )+6 e^x x \log (x)}{-5 x+e^x \left (10 x-2 x^2-2 x \log (3)\right )+2 e^x x \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.07, size = 30, normalized size = 1.30 \begin {gather*} 3 \, x + 3 \, \log \left (-{\left (2 \, {\left (x + \log \relax (3) - 5\right )} e^{x} - 2 \, e^{x} \log \relax (x) + 5\right )} e^{\left (-x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 26, normalized size = 1.13 \begin {gather*} 3 \, \log \left (2 \, x e^{x} + 2 \, e^{x} \log \relax (3) - 2 \, e^{x} \log \relax (x) - 10 \, e^{x} + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 27, normalized size = 1.17
method | result | size |
norman | \(3 \ln \left (2 \ln \relax (3) {\mathrm e}^{x}+2 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} \ln \relax (x )-10 \,{\mathrm e}^{x}+5\right )\) | \(27\) |
risch | \(3 x +3 \ln \left (\ln \relax (x )-\frac {\left (2 \ln \relax (3) {\mathrm e}^{x}+2 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{x}+5\right ) {\mathrm e}^{-x}}{2}\right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.68, size = 46, normalized size = 2.00 \begin {gather*} 3 \, \log \left (-x - \log \relax (3) + \log \relax (x) + 5\right ) + 3 \, \log \left (\frac {2 \, {\left (x + \log \relax (3) - \log \relax (x) - 5\right )} e^{x} + 5}{2 \, {\left (x + \log \relax (3) - \log \relax (x) - 5\right )}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^x\,\left (24\,x-6\,x\,\ln \relax (3)-6\,x^2+6\right )+6\,x\,{\mathrm {e}}^x\,\ln \relax (x)}{5\,x+{\mathrm {e}}^x\,\left (2\,x\,\ln \relax (3)-10\,x+2\,x^2\right )-2\,x\,{\mathrm {e}}^x\,\ln \relax (x)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.82, size = 36, normalized size = 1.57 \begin {gather*} 3 \log {\left (e^{x} + \frac {5}{2 x - 2 \log {\relax (x )} - 10 + 2 \log {\relax (3 )}} \right )} + 3 \log {\left (- x + \log {\relax (x )} - \log {\relax (3 )} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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