Optimal. Leaf size=16 \[ -1+\frac {x \log (x)}{\log (4+x-\log (x))} \]
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Rubi [F] time = 0.88, 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 {(-1+x) \log (x)+\left (-4-x+(-3-x) \log (x)+\log ^2(x)\right ) \log (4+x-\log (x))}{(-4-x+\log (x)) \log ^2(4+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 \left (-\frac {(-1+x) \log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))}+\frac {1+\log (x)}{\log (4+x-\log (x))}\right ) \, dx\\ &=-\int \frac {(-1+x) \log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))} \, dx+\int \frac {1+\log (x)}{\log (4+x-\log (x))} \, dx\\ &=-\int \left (-\frac {\log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))}+\frac {x \log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))}\right ) \, dx+\int \left (\frac {1}{\log (4+x-\log (x))}+\frac {\log (x)}{\log (4+x-\log (x))}\right ) \, dx\\ &=\int \frac {\log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))} \, dx-\int \frac {x \log (x)}{(4+x-\log (x)) \log ^2(4+x-\log (x))} \, dx+\int \frac {1}{\log (4+x-\log (x))} \, dx+\int \frac {\log (x)}{\log (4+x-\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 14, normalized size = 0.88 \begin {gather*} \frac {x \log (x)}{\log (4+x-\log (x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 14, normalized size = 0.88 \begin {gather*} \frac {x \log \relax (x)}{\log \left (x - \log \relax (x) + 4\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 = 0.88 \begin {gather*} \frac {x \log \relax (x)}{\log \left (x - \log \relax (x) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.94
method | result | size |
risch | \(\frac {x \ln \relax (x )}{\ln \left (-\ln \relax (x )+4+x \right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 14, normalized size = 0.88 \begin {gather*} \frac {x \log \relax (x)}{\log \left (x - \log \relax (x) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.74, size = 82, normalized size = 5.12 \begin {gather*} x+3\,\ln \relax (x)+\frac {5}{x-1}-{\ln \relax (x)}^2\,\left (\frac {1}{x-1}+1\right )+\frac {x\,\ln \relax (x)-\frac {x\,\ln \left (x-\ln \relax (x)+4\right )\,\left (\ln \relax (x)+1\right )\,\left (x-\ln \relax (x)+4\right )}{x-1}}{\ln \left (x-\ln \relax (x)+4\right )}+\frac {\ln \relax (x)\,\left (x^2+3\right )}{x-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 12, normalized size = 0.75 \begin {gather*} \frac {x \log {\relax (x )}}{\log {\left (x - \log {\relax (x )} + 4 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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