Optimal. Leaf size=31 \[ \log \left (\log \left (-x+\frac {-x+5 e^x x^2 (3-\log (x))}{3 x}\right )\right ) \]
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Rubi [F] time = 9.20, 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 {3+e^x (-10-15 x)+e^x (5+5 x) \log (x)}{\left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2+3 x-\log (x)-x \log (x)}{x (3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {-2-9 x^2+\log (x)+x \log (x)+3 x^2 \log (x)}{x (3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}\right ) \, dx\\ &=\int \frac {2+3 x-\log (x)-x \log (x)}{x (3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+\int \frac {-2-9 x^2+\log (x)+x \log (x)+3 x^2 \log (x)}{x (3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx\\ &=\int \left (\frac {3}{(3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {2}{x (3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {\log (x)}{(-3+\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {\log (x)}{x (-3+\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}\right ) \, dx+\int \left (\frac {2}{x (-3+\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {9 x}{(-3+\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {\log (x)}{(3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {\log (x)}{x (3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}+\frac {3 x \log (x)}{(3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )}\right ) \, dx\\ &=2 \int \frac {1}{x (3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+2 \int \frac {1}{x (-3+\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+3 \int \frac {1}{(3-\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+3 \int \frac {x \log (x)}{(3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+9 \int \frac {x}{(-3+\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+\int \frac {\log (x)}{(-3+\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+\int \frac {\log (x)}{x (-3+\log (x)) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+\int \frac {\log (x)}{(3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx+\int \frac {\log (x)}{x (3-\log (x)) \left (1+3 x-15 e^x x+5 e^x x \log (x)\right ) \log \left (\frac {1}{3} \left (-1-3 x+15 e^x x-5 e^x x \log (x)\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.85, size = 25, normalized size = 0.81 \begin {gather*} \log \left (\log \left (-\frac {1}{3}+\left (-1+5 e^x\right ) x-\frac {5}{3} e^x x \log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 19, normalized size = 0.61 \begin {gather*} \log \left (\log \left (-\frac {5}{3} \, x e^{x} \log \relax (x) + 5 \, x e^{x} - x - \frac {1}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 24, normalized size = 0.77 \begin {gather*} \log \left (\log \relax (3) - \log \left (-5 \, x e^{x} \log \relax (x) + 15 \, x e^{x} - 3 \, x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.65
method | result | size |
risch | \(\ln \left (\ln \left (-\frac {5 x \,{\mathrm e}^{x} \ln \relax (x )}{3}+5 \,{\mathrm e}^{x} x -x -\frac {1}{3}\right )\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.95, size = 24, normalized size = 0.77 \begin {gather*} \log \left (-\log \relax (3) + \log \left (-5 \, x e^{x} \log \relax (x) + 15 \, x e^{x} - 3 \, x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.05, size = 19, normalized size = 0.61 \begin {gather*} \ln \left (\ln \left (5\,x\,{\mathrm {e}}^x-x-\frac {5\,x\,{\mathrm {e}}^x\,\ln \relax (x)}{3}-\frac {1}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.32, size = 26, normalized size = 0.84 \begin {gather*} \log {\left (\log {\left (- \frac {5 x e^{x} \log {\relax (x )}}{3} + 5 x e^{x} - x - \frac {1}{3} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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