Optimal. Leaf size=27 \[ x \left (-x+x \left (-2+\frac {3}{x}+4 x^4-\log \left (\log \left (x^3\right )\right )\right )\right ) \]
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Rubi [A]
time = 0.10, antiderivative size = 24, normalized size of antiderivative = 0.89, number of steps
used = 7, number of rules used = 4, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6820, 2347,
2209, 2602} \begin {gather*} 4 x^6-3 x^2-x^2 \log \left (\log \left (x^3\right )\right )+3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2347
Rule 2602
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3-6 x+24 x^5-\frac {3 x}{\log \left (x^3\right )}-2 x \log \left (\log \left (x^3\right )\right )\right ) \, dx\\ &=3 x-3 x^2+4 x^6-2 \int x \log \left (\log \left (x^3\right )\right ) \, dx-3 \int \frac {x}{\log \left (x^3\right )} \, dx\\ &=3 x-3 x^2+4 x^6-x^2 \log \left (\log \left (x^3\right )\right )+3 \int \frac {x}{\log \left (x^3\right )} \, dx-\frac {x^2 \text {Subst}\left (\int \frac {e^{2 x/3}}{x} \, dx,x,\log \left (x^3\right )\right )}{\left (x^3\right )^{2/3}}\\ &=3 x-3 x^2+4 x^6-\frac {x^2 \text {Ei}\left (\frac {2 \log \left (x^3\right )}{3}\right )}{\left (x^3\right )^{2/3}}-x^2 \log \left (\log \left (x^3\right )\right )+\frac {x^2 \text {Subst}\left (\int \frac {e^{2 x/3}}{x} \, dx,x,\log \left (x^3\right )\right )}{\left (x^3\right )^{2/3}}\\ &=3 x-3 x^2+4 x^6-x^2 \log \left (\log \left (x^3\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 24, normalized size = 0.89 \begin {gather*} 3 x-3 x^2+4 x^6-x^2 \log \left (\log \left (x^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {-2 x \ln \left (x^{3}\right ) \ln \left (\ln \left (x^{3}\right )\right )+\left (24 x^{5}-6 x +3\right ) \ln \left (x^{3}\right )-3 x}{\ln \left (x^{3}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 29, normalized size = 1.07 \begin {gather*} 4 \, x^{6} - x^{2} \log \left (3\right ) - x^{2} \log \left (\log \left (x\right )\right ) - 3 \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 24, normalized size = 0.89 \begin {gather*} 4 \, x^{6} - x^{2} \log \left (\log \left (x^{3}\right )\right ) - 3 \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 22, normalized size = 0.81 \begin {gather*} 4 x^{6} - x^{2} \log {\left (\log {\left (x^{3} \right )} \right )} - 3 x^{2} + 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 0.89 \begin {gather*} 4 \, x^{6} - x^{2} \log \left (\log \left (x^{3}\right )\right ) - 3 \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.73, size = 24, normalized size = 0.89 \begin {gather*} 3\,x-3\,x^2+4\,x^6-x^2\,\ln \left (\ln \left (x^3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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