Optimal. Leaf size=10 \[ 11+x+x (-5+\log (\log (x))) \]
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Rubi [A]
time = 0.02, antiderivative size = 9, normalized size of antiderivative = 0.90, number of steps
used = 5, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {6820, 2335,
2600} \begin {gather*} x \log (\log (x))-4 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2335
Rule 2600
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4+\frac {1}{\log (x)}+\log (\log (x))\right ) \, dx\\ &=-4 x+\int \frac {1}{\log (x)} \, dx+\int \log (\log (x)) \, dx\\ &=-4 x+x \log (\log (x))+\text {li}(x)-\int \frac {1}{\log (x)} \, dx\\ &=-4 x+x \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 0.90 \begin {gather*} -4 x+x \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 10, normalized size = 1.00
method | result | size |
default | \(-4 x +x \ln \left (\ln \left (x \right )\right )\) | \(10\) |
norman | \(-4 x +x \ln \left (\ln \left (x \right )\right )\) | \(10\) |
risch | \(-4 x +x \ln \left (\ln \left (x \right )\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 9, normalized size = 0.90 \begin {gather*} x \log \left (\log \left (x\right )\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 9, normalized size = 0.90 \begin {gather*} x \log \left (\log \left (x\right )\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 8, normalized size = 0.80 \begin {gather*} x \log {\left (\log {\left (x \right )} \right )} - 4 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 9, normalized size = 0.90 \begin {gather*} x \log \left (\log \left (x\right )\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.06, size = 7, normalized size = 0.70 \begin {gather*} x\,\left (\ln \left (\ln \left (x\right )\right )-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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