Optimal. Leaf size=18 \[ -4+x+\log \left (-x+x^2+\log \left (\frac {120}{\log (x)}\right )\right ) \]
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Rubi [A] time = 0.68, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps used = 5, number of rules used = 4, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {6741, 6688, 6742, 6684} \begin {gather*} \log \left (-x^2+x-\log \left (\frac {120}{\log (x)}\right )\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6688
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1-\left (-x+x^2+x^3\right ) \log (x)-x \log (x) \log \left (\frac {120}{\log (x)}\right )}{x \log (x) \left (x-x^2-\log \left (\frac {120}{\log (x)}\right )\right )} \, dx\\ &=\int \frac {-1+x \log (x) \left (-1+x+x^2+\log \left (\frac {120}{\log (x)}\right )\right )}{x \log (x) \left ((-1+x) x+\log \left (\frac {120}{\log (x)}\right )\right )} \, dx\\ &=\int \left (1+\frac {-1-x \log (x)+2 x^2 \log (x)}{x \log (x) \left (-x+x^2+\log \left (\frac {120}{\log (x)}\right )\right )}\right ) \, dx\\ &=x+\int \frac {-1-x \log (x)+2 x^2 \log (x)}{x \log (x) \left (-x+x^2+\log \left (\frac {120}{\log (x)}\right )\right )} \, dx\\ &=x+\log \left (x-x^2-\log \left (\frac {120}{\log (x)}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 17, normalized size = 0.94 \begin {gather*} x+\log \left (-x+x^2+\log \left (\frac {120}{\log (x)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 17, normalized size = 0.94 \begin {gather*} x + \log \left (x^{2} - x + \log \left (\frac {120}{\log \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.53, size = 17, normalized size = 0.94 \begin {gather*} x + \log \left (-x^{2} + x - \log \left (120\right ) + \log \left (\log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.28, size = 37, normalized size = 2.06
method | result | size |
risch | \(x +\ln \left (\ln \left (\ln \relax (x )\right )+\frac {i \left (2 i x^{2}+2 i \ln \relax (5)+6 i \ln \relax (2)+2 i \ln \relax (3)-2 i x \right )}{2}\right )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 25, normalized size = 1.39 \begin {gather*} x + \log \left (-x^{2} + x - \log \relax (5) - \log \relax (3) - 3 \, \log \relax (2) + \log \left (\log \relax (x)\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 = -0.06 \begin {gather*} -\int \frac {\ln \relax (x)\,\left (x^3+x^2-x\right )+x\,\ln \left (\frac {120}{\ln \relax (x)}\right )\,\ln \relax (x)-1}{\ln \relax (x)\,\left (x^2-x^3\right )-x\,\ln \left (\frac {120}{\ln \relax (x)}\right )\,\ln \relax (x)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 14, normalized size = 0.78 \begin {gather*} x + \log {\left (x^{2} - x + \log {\left (\frac {120}{\log {\relax (x )}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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