Optimal. Leaf size=18 \[ 25+\frac {x}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \]
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Rubi [F]
time = 0.14, 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 {-3+\log \left (\frac {x^3}{3+\log (21)}\right ) \log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\frac {3}{\log \left (\frac {x^3}{3+\log (21)}\right )}+\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}{\log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\\ &=\int \left (-\frac {3}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}+\frac {1}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}\right ) \, dx\\ &=-\left (3 \int \frac {1}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\right )+\int \frac {1}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 16, normalized size = 0.89 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 3.38, size = 17, normalized size = 0.94
method | result | size |
norman | \(\frac {x}{\ln \left (\ln \left (\frac {x^{3}}{\ln \left (21\right )+3}\right )\right )}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 19, normalized size = 1.06 \begin {gather*} \frac {x}{\log \left (3 \, \log \left (x\right ) - \log \left (\log \left (7\right ) + \log \left (3\right ) + 3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.89 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x^{3}}{\log \left (21\right ) + 3}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.67 \begin {gather*} \frac {x}{\log {\left (\log {\left (\frac {x^{3}}{3 + \log {\left (21 \right )}} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (18) = 36\).
time = 0.42, size = 44, normalized size = 2.44 \begin {gather*} \frac {x \log \left (x^{3}\right ) - x \log \left (\log \left (21\right ) + 3\right )}{\log \left (\frac {x^{3}}{\log \left (21\right ) + 3}\right ) \log \left (\log \left (x^{3}\right ) - \log \left (\log \left (21\right ) + 3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.89, size = 17, normalized size = 0.94 \begin {gather*} \frac {x}{\ln \left (\ln \left (x^3\right )-\ln \left (\ln \left (21\right )+3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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