Optimal. Leaf size=22 \[ 5 \left (-x+x \log \left (\frac {x^4}{18}\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )\right ) \]
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Rubi [F]
time = 0.16, 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 {10 \log \left (\frac {x^4}{18}\right )-5 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left (20 \log \left (x^2\right )+5 \log \left (x^2\right ) \log \left (\frac {x^4}{18}\right )\right ) \log \left (\log \left (x^2\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\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 5 \left (-1+\frac {2 \log \left (\frac {x^4}{18}\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}+\left (4+\log \left (\frac {x^4}{18}\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )\right ) \, dx\\ &=5 \int \left (-1+\frac {2 \log \left (\frac {x^4}{18}\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}+\left (4+\log \left (\frac {x^4}{18}\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )\right ) \, dx\\ &=-5 x+5 \int \left (4+\log \left (\frac {x^4}{18}\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right ) \, dx+10 \int \frac {\log \left (\frac {x^4}{18}\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx\\ &=-5 x+5 \int \left (4 \log \left (\log \left (\log \left (x^2\right )\right )\right )+\log \left (\frac {x^4}{18}\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )\right ) \, dx+10 \int \frac {\log \left (\frac {x^4}{18}\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx\\ &=-5 x+5 \int \log \left (\frac {x^4}{18}\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right ) \, dx+10 \int \frac {\log \left (\frac {x^4}{18}\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+20 \int \log \left (\log \left (\log \left (x^2\right )\right )\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 21, normalized size = 0.95 \begin {gather*} -5 x+5 x \log \left (\frac {x^4}{18}\right ) \log \left (\log \left (\log \left (x^2\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 = 0.55, size = 265, normalized size = 12.05
method | result | size |
risch | \(\left (20 x \ln \left (x \right )-\frac {5 i \pi x \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {5 i \pi x \mathrm {csgn}\left (i x^{3}\right )^{3}}{2}-\frac {5 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-\frac {5 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}+\frac {5 i \pi x \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )^{2}}{2}-\frac {5 i \pi x \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right ) \mathrm {csgn}\left (i x \right )}{2}+\frac {5 i \pi x \mathrm {csgn}\left (i x^{4}\right )^{2} \mathrm {csgn}\left (i x \right )}{2}+\frac {5 i \pi x \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {5 i \pi x \mathrm {csgn}\left (i x^{4}\right )^{3}}{2}+\frac {5 i \pi x \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x \right )}{2}+5 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-10 x \ln \left (3\right )-5 x \ln \left (2\right )\right ) \ln \left (\ln \left (2 \ln \left (x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )\right )-5 x\) | \(265\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 28, normalized size = 1.27 \begin {gather*} -5 \, {\left (x {\left (2 \, \log \left (3\right ) + \log \left (2\right )\right )} - 4 \, x \log \left (x\right )\right )} \log \left (\log \left (2\right ) + \log \left (\log \left (x\right )\right )\right ) - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 24, normalized size = 1.09 \begin {gather*} -5 \, {\left (x \log \left (18\right ) - 2 \, x \log \left (x^{2}\right )\right )} \log \left (\log \left (\log \left (x^{2}\right )\right )\right ) - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.45, size = 26, normalized size = 1.18 \begin {gather*} - 5 x + \left (10 x \log {\left (x^{2} \right )} - 5 x \log {\left (18 \right )}\right ) \log {\left (\log {\left (\log {\left (x^{2} \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 24, normalized size = 1.09 \begin {gather*} -5 \, {\left (x \log \left (18\right ) - 2 \, x \log \left (x^{2}\right )\right )} \log \left (\log \left (\log \left (x^{2}\right )\right )\right ) - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.82, size = 31, normalized size = 1.41 \begin {gather*} -5\,x-\ln \left (\ln \left (\ln \left (x^2\right )\right )\right )\,\left (20\,x+x\,\left (5\,\ln \left (18\right )-20\right )-10\,x\,\ln \left (x^2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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