Optimal. Leaf size=24 \[ \frac {e^{40+e^4-x^2 \log ^2(3 x)}}{\log (\log (x))} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(24)=48\).
time = 1.10, antiderivative size = 52, normalized size of antiderivative = 2.17, number of steps
used = 2, number of rules used = 2, integrand size = 81, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6820, 2326}
\begin {gather*} \frac {x e^{-x^2 \log ^2(3 x)+e^4+40} \log (3 x) (\log (3 x)+1)}{\left (x \log ^2(3 x)+x \log (3 x)\right ) \log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{40 \left (1+\frac {e^4}{40}\right )-x^2 \log ^2(3 x)} \left (-1-2 x^2 \log (x) \log (3 x) (1+\log (3 x)) \log (\log (x))\right )}{x \log (x) \log ^2(\log (x))} \, dx\\ &=\frac {e^{40+e^4-x^2 \log ^2(3 x)} x \log (3 x) (1+\log (3 x))}{\left (x \log (3 x)+x \log ^2(3 x)\right ) \log (\log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 24, normalized size = 1.00 \begin {gather*} \frac {e^{40+e^4-x^2 \log ^2(3 x)}}{\log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 39, normalized size = 1.62
method | result | size |
risch | \(\frac {x^{-2 x^{2} \ln \left (3\right )} {\mathrm e}^{-x^{2} \ln \left (3\right )^{2}+40-x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{4}}}{\ln \left (\ln \left (x \right )\right )}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 38, normalized size = 1.58 \begin {gather*} \frac {e^{\left (-x^{2} \log \left (3\right )^{2} - 2 \, x^{2} \log \left (3\right ) \log \left (x\right ) - x^{2} \log \left (x\right )^{2} + e^{4} + 40\right )}}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 38, normalized size = 1.58 \begin {gather*} \frac {e^{\left (-x^{2} \log \left (3\right )^{2} - 2 \, x^{2} \log \left (3\right ) \log \left (x\right ) - x^{2} \log \left (x\right )^{2} + e^{4} + 40\right )}}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 22, normalized size = 0.92 \begin {gather*} \frac {e^{- x^{2} \left (\log {\left (x \right )} + \log {\left (3 \right )}\right )^{2} + 40 + e^{4}}}{\log {\left (\log {\left (x \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 38, normalized size = 1.58 \begin {gather*} \frac {e^{\left (-x^{2} \log \left (3\right )^{2} - 2 \, x^{2} \log \left (3\right ) \log \left (x\right ) - x^{2} \log \left (x\right )^{2} + e^{4} + 40\right )}}{\log \left (\log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.83, size = 42, normalized size = 1.75 \begin {gather*} \frac {{\mathrm {e}}^{40}\,{\mathrm {e}}^{-x^2\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}\,{\mathrm {e}}^{-x^2\,{\ln \left (x\right )}^2}}{x^{2\,x^2\,\ln \left (3\right )}\,\ln \left (\ln \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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