Optimal. Leaf size=14 \[ \log \left (\log \left (-22-\log \left (\sqrt [3]{2} x\right )\right )\right ) \]
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Rubi [A]
time = 0.06, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {2437, 2339, 29}
\begin {gather*} \log \left (\log \left (-\log \left (\sqrt [3]{2} x\right )-22\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 2437
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {1}{(22+x) \log (-22-x)} \, dx,x,\log \left (\sqrt [3]{2} x\right )\right )\\ &=\text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,-22-\log \left (\sqrt [3]{2} x\right )\right )\\ &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (-22-\log \left (\sqrt [3]{2} x\right )\right )\right )\\ &=\log \left (\log \left (-22-\log \left (\sqrt [3]{2} x\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.12, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (22 x+x \log \left (\sqrt [3]{2} x\right )\right ) \log \left (-22-\log \left (\sqrt [3]{2} x\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 20.79, size = 13, normalized size = 0.93
method | result | size |
norman | \(\ln \left (\ln \left (-\ln \left (x 2^{\frac {1}{3}}\right )-22\right )\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.48, size = 17, normalized size = 1.21 \begin {gather*} \log \left (-\log \left (3\right ) + \log \left (-\log \left (2\right ) - 3 \, \log \left (x\right ) - 66\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 12, normalized size = 0.86 \begin {gather*} \log \left (\log \left (-\log \left (2^{\frac {1}{3}} x\right ) - 22\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 1.00 \begin {gather*} \log {\left (\log {\left (- \log {\left (\sqrt [3]{2} x \right )} - 22 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 1.21 \begin {gather*} \log \left (\log \left (3\right ) - \log \left (-\log \left (2\right ) - 3 \, \log \left (x\right ) - 66\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.14, size = 12, normalized size = 0.86 \begin {gather*} \ln \left (\ln \left (-\ln \left (2^{1/3}\,x\right )-22\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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