Optimal. Leaf size=30 \[ 2-e^{e^{\frac {e^{x/9}}{18-\log ^2(5)}}+x}+\log (2) \]
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Rubi [A]
time = 0.35, antiderivative size = 26, normalized size of antiderivative = 0.87, number of steps
used = 3, number of rules used = 3, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12, 2320, 2326}
\begin {gather*} -e^{x+e^{\frac {e^{x/9}}{18-\log ^2(5)}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2320
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\int e^{e^{-\frac {e^{x/9}}{-18+\log ^2(5)}}+x} \left (162+e^{\frac {x}{9}-\frac {e^{x/9}}{-18+\log ^2(5)}}-9 \log ^2(5)\right ) \, dx}{9 \left (18-\log ^2(5)\right )}\\ &=-\frac {\text {Subst}\left (\int e^{e^{-\frac {x}{-18+\log ^2(5)}}} x^8 \left (e^{-\frac {x}{-18+\log ^2(5)}} x+162 \left (1-\frac {\log ^2(5)}{18}\right )\right ) \, dx,x,e^{x/9}\right )}{18-\log ^2(5)}\\ &=-e^{e^{\frac {e^{x/9}}{18-\log ^2(5)}}+x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 25, normalized size = 0.83 \begin {gather*} -e^{e^{-\frac {e^{x/9}}{-18+\log ^2(5)}}+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.76, size = 21, normalized size = 0.70
method | result | size |
norman | \(-{\mathrm e}^{{\mathrm e}^{-\frac {{\mathrm e}^{\frac {x}{9}}}{\ln \left (5\right )^{2}-18}}+x}\) | \(21\) |
risch | \(-\frac {9 \,{\mathrm e}^{{\mathrm e}^{-\frac {{\mathrm e}^{\frac {x}{9}}}{\ln \left (5\right )^{2}-18}}+x} \ln \left (5\right )^{2}}{9 \ln \left (5\right )^{2}-162}+\frac {162 \,{\mathrm e}^{{\mathrm e}^{-\frac {{\mathrm e}^{\frac {x}{9}}}{\ln \left (5\right )^{2}-18}}+x}}{9 \ln \left (5\right )^{2}-162}\) | \(66\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.58, size = 20, normalized size = 0.67 \begin {gather*} -e^{\left (x + e^{\left (-\frac {e^{\left (\frac {1}{9} \, x\right )}}{\log \left (5\right )^{2} - 18}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 42, normalized size = 1.40 \begin {gather*} -e^{\left ({\left (x e^{\left (\frac {1}{9} \, x\right )} + e^{\left (\frac {x \log \left (5\right )^{2} - 18 \, x - 9 \, e^{\left (\frac {1}{9} \, x\right )}}{9 \, {\left (\log \left (5\right )^{2} - 18\right )}}\right )}\right )} e^{\left (-\frac {1}{9} \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 19, normalized size = 0.63 \begin {gather*} - e^{x + e^{- \frac {e^{\frac {x}{9}}}{-18 + \log {\left (5 \right )}^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 20, normalized size = 0.67 \begin {gather*} -e^{\left (x + e^{\left (-\frac {e^{\left (\frac {1}{9} \, x\right )}}{\log \left (5\right )^{2} - 18}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.98, size = 20, normalized size = 0.67 \begin {gather*} -{\mathrm {e}}^x\,{\mathrm {e}}^{{\mathrm {e}}^{-\frac {{\mathrm {e}}^{x/9}}{{\ln \left (5\right )}^2-18}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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