Optimal. Leaf size=30 \[ \frac {4 e^{8-\frac {2 \left (e^{(3+x)^2}-x\right )}{x \log (\log (x))}}}{x^2} \]
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Rubi [B] time = 1.58, antiderivative size = 162, normalized size of antiderivative = 5.40, number of steps used = 1, number of rules used = 1, integrand size = 97, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2288} \begin {gather*} \frac {4 e^{-\frac {2 \left (e^{x^2+6 x+9}-x\right )}{x \log (\log (x))}} \left (e^{x^2+6 x+17}+e^{x^2+6 x+17} \left (-2 x^2-6 x+1\right ) \log (x) \log (\log (x))-e^8 x\right )}{x^4 \log (x) \left (\frac {e^{x^2+6 x+9}-x}{x^2 \log (x) \log ^2(\log (x))}+\frac {e^{x^2+6 x+9}-x}{x^2 \log (\log (x))}+\frac {1-2 e^{x^2+6 x+9} (x+3)}{x \log (\log (x))}\right ) \log ^2(\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{-\frac {2 \left (e^{9+6 x+x^2}-x\right )}{x \log (\log (x))}} \left (e^{17+6 x+x^2}-e^8 x+e^{17+6 x+x^2} \left (1-6 x-2 x^2\right ) \log (x) \log (\log (x))\right )}{x^4 \log (x) \left (\frac {e^{9+6 x+x^2}-x}{x^2 \log (x) \log ^2(\log (x))}+\frac {e^{9+6 x+x^2}-x}{x^2 \log (\log (x))}+\frac {1-2 e^{9+6 x+x^2} (3+x)}{x \log (\log (x))}\right ) \log ^2(\log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 29, normalized size = 0.97 \begin {gather*} \frac {4 e^{8+\frac {2-\frac {2 e^{(3+x)^2}}{x}}{\log (\log (x))}}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 36, normalized size = 1.20 \begin {gather*} \frac {4 \, e^{\left (\frac {2 \, {\left (x e^{8} - e^{\left (x^{2} + 6 \, x + 17\right )}\right )} e^{\left (-8\right )}}{x \log \left (\log \relax (x)\right )} + 8\right )}}{x^{2}} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 33, normalized size = 1.10
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{\frac {8 x \ln \left (\ln \relax (x )\right )-2 \,{\mathrm e}^{\left (3+x \right )^{2}}+2 x}{x \ln \left (\ln \relax (x )\right )}}}{x^{2}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 34, normalized size = 1.13 \begin {gather*} \frac {4 \, e^{\left (-\frac {2 \, e^{\left (x^{2} + 6 \, x + 9\right )}}{x \log \left (\log \relax (x)\right )} + \frac {2}{\log \left (\log \relax (x)\right )} + 8\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.50, size = 36, normalized size = 1.20 \begin {gather*} \frac {4\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^9}{x\,\ln \left (\ln \relax (x)\right )}}\,{\mathrm {e}}^8\,{\mathrm {e}}^{\frac {2}{\ln \left (\ln \relax (x)\right )}}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.95, size = 31, normalized size = 1.03 \begin {gather*} \frac {4 e^{8} e^{- \frac {2 \left (- x + e^{x^{2} + 6 x + 9}\right )}{x \log {\left (\log {\relax (x )} \right )}}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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