Optimal. Leaf size=32 \[ \log \left (\frac {4 \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{-\frac {2}{x}+\frac {3 x}{5}}\right ) \]
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Rubi [A]
time = 2.98, antiderivative size = 30, normalized size of antiderivative = 0.94, number of steps
used = 7, number of rules used = 5, integrand size = 122, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {1607, 6857,
457, 78, 6816} \begin {gather*} -\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rule 457
Rule 1607
Rule 6816
Rule 6857
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{x \left (-10+3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx\\ &=\int \left (\frac {-10-3 x^2}{x \left (-10+3 x^2\right )}-\frac {2 (-1+\log (x) \log (4 \log (x)))}{x \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}\right ) \, dx\\ &=-\left (2 \int \frac {-1+\log (x) \log (4 \log (x))}{x \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx\right )+\int \frac {-10-3 x^2}{x \left (-10+3 x^2\right )} \, dx\\ &=\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\frac {1}{2} \text {Subst}\left (\int \frac {-10-3 x}{x (-10+3 x)} \, dx,x,x^2\right )\\ &=\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\frac {1}{2} \text {Subst}\left (\int \left (\frac {1}{x}-\frac {6}{-10+3 x}\right ) \, dx,x,x^2\right )\\ &=\log (x)-\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 30, normalized size = 0.94 \begin {gather*} \log (x)-\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 39.48, size = 892, normalized size = 27.88
method | result | size |
risch | \(\text {Expression too large to display}\) | \(892\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 31, normalized size = 0.97 \begin {gather*} -\log \left (3 \, x^{2} - 10\right ) + \log \left (x\right ) + \log \left (\log \left (\log \left (2\right ) + \log \left (x\right ) - \log \left (2 \, \log \left (2\right ) + \log \left (\log \left (x\right )\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 28, normalized size = 0.88 \begin {gather*} -\log \left (3 \, x^{2} - 10\right ) + \log \left (x\right ) + \log \left (\log \left (\log \left (\frac {\log \left (4 \, \log \left (x\right )\right )}{2 \, x}\right )^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.53, size = 27, normalized size = 0.84 \begin {gather*} \log {\left (x \right )} - \log {\left (3 x^{2} - 10 \right )} + \log {\left (\log {\left (\log {\left (\frac {\log {\left (4 \log {\left (x \right )} \right )}}{2 x} \right )}^{2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.25, size = 26, normalized size = 0.81 \begin {gather*} \ln \left (\ln \left ({\ln \left (\frac {\ln \left (4\,\ln \left (x\right )\right )}{2\,x}\right )}^2\right )\right )-\ln \left (x^2-\frac {10}{3}\right )+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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