Optimal. Leaf size=15 \[ 1+x-(-3+x) (3-\log (\log (x))) \]
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Rubi [A] time = 0.11, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 9, number of rules used = 6, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.261, Rules used = {6688, 2353, 2298, 2302, 29, 2520} \begin {gather*} -2 x+x \log (\log (x))-3 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2298
Rule 2302
Rule 2353
Rule 2520
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {-3+x}{x \log (x)}+\log (\log (x))\right ) \, dx\\ &=-2 x+\int \frac {-3+x}{x \log (x)} \, dx+\int \log (\log (x)) \, dx\\ &=-2 x+x \log (\log (x))+\int \left (\frac {1}{\log (x)}-\frac {3}{x \log (x)}\right ) \, dx-\int \frac {1}{\log (x)} \, dx\\ &=-2 x+x \log (\log (x))-\text {li}(x)-3 \int \frac {1}{x \log (x)} \, dx+\int \frac {1}{\log (x)} \, dx\\ &=-2 x+x \log (\log (x))-3 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-2 x-3 \log (\log (x))+x \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 14, normalized size = 0.93 \begin {gather*} -2 x-3 \log (\log (x))+x \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 11, normalized size = 0.73 \begin {gather*} {\left (x - 3\right )} \log \left (\log \relax (x)\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 14, normalized size = 0.93 \begin {gather*} x \log \left (\log \relax (x)\right ) - 2 \, x - 3 \, \log \left (\log \relax (x)\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 = 1.00
method | result | size |
default | \(-2 x -3 \ln \left (\ln \relax (x )\right )+x \ln \left (\ln \relax (x )\right )\) | \(15\) |
norman | \(-2 x -3 \ln \left (\ln \relax (x )\right )+x \ln \left (\ln \relax (x )\right )\) | \(15\) |
risch | \(-2 x -3 \ln \left (\ln \relax (x )\right )+x \ln \left (\ln \relax (x )\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 14, normalized size = 0.93 \begin {gather*} x \log \left (\log \relax (x)\right ) - 2 \, x - 3 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.83, size = 14, normalized size = 0.93 \begin {gather*} x\,\ln \left (\ln \relax (x)\right )-3\,\ln \left (\ln \relax (x)\right )-2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 15, normalized size = 1.00 \begin {gather*} x \log {\left (\log {\relax (x )} \right )} - 2 x - 3 \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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