Optimal. Leaf size=29 \[ \frac {4 e^{-x^2 \left (e^{3-e^{2 x}}+\log (\log (4))\right )^2}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(200\) vs. \(2(29)=58\).
time = 1.79, antiderivative size = 200, normalized size of antiderivative = 6.90, number of steps
used = 1, number of rules used = 1, integrand size = 123, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2326}
\begin {gather*} \frac {4 e^{-e^{6-2 e^{2 x}} x^2-x^2 \log ^2(\log (4))} \log ^{-2 e^{3-e^{2 x}} x^2}(4) \left (x^2 \log ^2(\log (4))+e^{6-2 e^{2 x}} \left (x^2-2 e^{2 x} x^3\right )+2 e^{3-e^{2 x}} \left (x^2-e^{2 x} x^3\right ) \log (\log (4))\right )}{x^2 \left (-2 e^{2 x-2 e^{2 x}+6} x^2-2 e^{2 x-e^{2 x}+3} x^2 \log (\log (4))+e^{6-2 e^{2 x}} x+x \log ^2(\log (4))+2 e^{3-e^{2 x}} x \log (\log (4))\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{-e^{6-2 e^{2 x}} x^2-x^2 \log ^2(\log (4))} \log ^{-2 e^{3-e^{2 x}} x^2}(4) \left (e^{6-2 e^{2 x}} \left (x^2-2 e^{2 x} x^3\right )+2 e^{3-e^{2 x}} \left (x^2-e^{2 x} x^3\right ) \log (\log (4))+x^2 \log ^2(\log (4))\right )}{x^2 \left (e^{6-2 e^{2 x}} x-2 e^{6-2 e^{2 x}+2 x} x^2+2 e^{3-e^{2 x}} x \log (\log (4))-2 e^{3-e^{2 x}+2 x} x^2 \log (\log (4))+x \log ^2(\log (4))\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.16, size = 48, normalized size = 1.66 \begin {gather*} \frac {4 e^{-x^2 \left (e^{6-2 e^{2 x}}+\log ^2(\log (4))\right )} \log ^{-2 e^{3-e^{2 x}} x^2}(4)}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs.
\(2(29)=58\).
time = 0.24, size = 65, normalized size = 2.24
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{-x^{2} \left (\ln \left (2\right )^{2}+2 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )+2 \,{\mathrm e}^{3-{\mathrm e}^{2 x}} \ln \left (2\right )+\ln \left (\ln \left (2\right )\right )^{2}+2 \,{\mathrm e}^{3-{\mathrm e}^{2 x}} \ln \left (\ln \left (2\right )\right )+{\mathrm e}^{6-2 \,{\mathrm e}^{2 x}}\right )}}{x}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 83 vs.
\(2 (28) = 56\).
time = 0.58, size = 83, normalized size = 2.86 \begin {gather*} \frac {4 \, e^{\left (-2 \, x^{2} e^{\left (-e^{\left (2 \, x\right )} + 3\right )} \log \left (2\right ) - x^{2} \log \left (2\right )^{2} - 2 \, x^{2} e^{\left (-e^{\left (2 \, x\right )} + 3\right )} \log \left (\log \left (2\right )\right ) - 2 \, x^{2} \log \left (2\right ) \log \left (\log \left (2\right )\right ) - x^{2} \log \left (\log \left (2\right )\right )^{2} - x^{2} e^{\left (-2 \, e^{\left (2 \, x\right )} + 6\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 52, normalized size = 1.79 \begin {gather*} \frac {4 \, e^{\left (-2 \, x^{2} e^{\left (-e^{\left (2 \, x\right )} + 3\right )} \log \left (2 \, \log \left (2\right )\right ) - x^{2} \log \left (2 \, \log \left (2\right )\right )^{2} - x^{2} e^{\left (-2 \, e^{\left (2 \, x\right )} + 6\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (24) = 48\).
time = 0.33, size = 51, normalized size = 1.76 \begin {gather*} \frac {4 e^{- 2 x^{2} e^{3 - e^{2 x}} \log {\left (2 \log {\left (2 \right )} \right )} - x^{2} e^{6 - 2 e^{2 x}} - x^{2} \log {\left (2 \log {\left (2 \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 [B]
time = 5.97, size = 90, normalized size = 3.10 \begin {gather*} \frac {4\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^6}\,{\mathrm {e}}^{-x^2\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-x^2\,{\ln \left (\ln \left (2\right )\right )}^2}}{2^{2\,x^2\,\ln \left (\ln \left (2\right )\right )}\,2^{2\,x^2\,{\mathrm {e}}^{-{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^3}\,x\,{\ln \left (2\right )}^{2\,x^2\,{\mathrm {e}}^{-{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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