Optimal. Leaf size=11 \[ -8 x+\frac {x}{\log (\log (x))} \]
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Rubi [F]
time = 0.06, 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+\log (x) \log (\log (x))-8 \log (x) \log ^2(\log (x))}{\log (x) \log ^2(\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 (-8-\frac {1}{\log (x) \log ^2(\log (x))}+\frac {1}{\log (\log (x))}\right ) \, dx\\ &=-8 x-\int \frac {1}{\log (x) \log ^2(\log (x))} \, dx+\int \frac {1}{\log (\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 11, normalized size = 1.00 \begin {gather*} -8 x+\frac {x}{\log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.95, size = 12, normalized size = 1.09
method | result | size |
risch | \(\frac {x}{\ln \left (\ln \left (x \right )\right )}-8 x\) | \(12\) |
norman | \(\frac {x -8 x \ln \left (\ln \left (x \right )\right )}{\ln \left (\ln \left (x \right )\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 11, normalized size = 1.00 \begin {gather*} -8 \, x + \frac {x}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 17, normalized size = 1.55 \begin {gather*} -\frac {8 \, x \log \left (\log \left (x\right )\right ) - x}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.73 \begin {gather*} - 8 x + \frac {x}{\log {\left (\log {\left (x \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 11, normalized size = 1.00 \begin {gather*} -8 \, x + \frac {x}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.28, size = 11, normalized size = 1.00 \begin {gather*} \frac {x}{\ln \left (\ln \left (x\right )\right )}-8\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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