Optimal. Leaf size=20 \[ \frac {3 e^{\log ^2\left (x^2 \log (x)\right )} (-2+\log (3))}{x} \]
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Rubi [A]
time = 0.08, antiderivative size = 38, normalized size of antiderivative = 1.90, number of steps
used = 1, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2326}
\begin {gather*} -\frac {3 e^{\log ^2\left (x^2 \log (x)\right )} (2 (2-\log (3)) \log (x)+2-\log (3))}{x+2 x \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {3 e^{\log ^2\left (x^2 \log (x)\right )} (2-\log (3)+2 (2-\log (3)) \log (x))}{x+2 x \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 20, normalized size = 1.00 \begin {gather*} \frac {3 e^{\log ^2\left (x^2 \log (x)\right )} (-2+\log (3))}{x} \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 = 0.12, size = 158, normalized size = 7.90
method | result | size |
risch | \(\frac {3 \left (\ln \left (3\right )-2\right ) {\mathrm e}^{\frac {\left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} \ln \left (x \right )\right )^{2}-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} \ln \left (x \right )\right ) \mathrm {csgn}\left (i \ln \left (x \right )\right )-i \pi \mathrm {csgn}\left (i x^{2} \ln \left (x \right )\right )^{3}+i \pi \mathrm {csgn}\left (i x^{2} \ln \left (x \right )\right )^{2} \mathrm {csgn}\left (i \ln \left (x \right )\right )+4 \ln \left (x \right )+2 \ln \left (\ln \left (x \right )\right )\right )^{2}}{4}}}{x}\) | \(158\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 29, normalized size = 1.45 \begin {gather*} \frac {3 \, {\left (\log \left (3\right ) - 2\right )} e^{\left (4 \, \log \left (x\right )^{2} + 4 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) + \log \left (\log \left (x\right )\right )^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 0.95 \begin {gather*} \frac {3 \, {\left (\log \left (3\right ) - 2\right )} e^{\left (\log \left (x^{2} \log \left (x\right )\right )^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 19, normalized size = 0.95 \begin {gather*} \frac {\left (-6 + 3 \log {\left (3 \right )}\right ) e^{\log {\left (x^{2} \log {\left (x \right )} \right )}^{2}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int -\frac {{\mathrm {e}}^{{\ln \left (x^2\,\ln \left (x\right )\right )}^2}\,\left (\ln \left (x\right )\,\left (3\,\ln \left (3\right )-6\right )-\ln \left (x^2\,\ln \left (x\right )\right )\,\left (6\,\ln \left (3\right )+\ln \left (x\right )\,\left (12\,\ln \left (3\right )-24\right )-12\right )\right )}{x^2\,\ln \left (x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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