Optimal. Leaf size=20 \[ \left (x+\frac {1}{2} \log (-3-3 x+\log (9))\right )^{e^{e^x}} \]
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Rubi [F] time = 6.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {2^{-e^{e^x}} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \left (e^{e^x} (-9-6 x+2 \log (9))+e^{e^x} \left (e^x \left (-6 x-6 x^2+2 x \log (9)\right )+e^x (-3-3 x+\log (9)) \log (-3-3 x+\log (9))\right ) \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right )\right )}{-6 x-6 x^2+2 x \log (9)+(-3-3 x+\log (9)) \log (-3-3 x+\log (9))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2^{-e^{e^x}} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \left (e^{e^x} (-9-6 x+2 \log (9))+e^{e^x} \left (e^x \left (-6 x-6 x^2+2 x \log (9)\right )+e^x (-3-3 x+\log (9)) \log (-3-3 x+\log (9))\right ) \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right )\right )}{-6 x^2+x (-6+2 \log (9))+(-3-3 x+\log (9)) \log (-3-3 x+\log (9))} \, dx\\ &=\int \frac {2^{-e^{e^x}} e^{e^x} (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}} \left (6 x+9 \left (1-\frac {4 \log (3)}{9}\right )+e^x (3+3 x-\log (9)) (2 x+\log (-3-3 x+\log (9))) \log \left (x+\frac {1}{2} \log (-3-3 x+\log (9))\right )\right )}{3+3 x-\log (9)} \, dx\\ &=\int \left (\frac {2^{-e^{e^x}} e^{e^x} (9+6 x-4 \log (3)) (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}}}{3+3 x-\log (9)}+2^{-e^{e^x}} e^{e^x+x} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right )\right ) \, dx\\ &=\int \frac {2^{-e^{e^x}} e^{e^x} (9+6 x-4 \log (3)) (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}}}{3+3 x-\log (9)} \, dx+\int 2^{-e^{e^x}} e^{e^x+x} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right ) \, dx\\ &=\int \left (2^{1-e^{e^x}} e^{e^x} (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}}+\frac {3\ 2^{-e^{e^x}} e^{e^x} (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}}}{3+3 x-\log (9)}\right ) \, dx+\int 2^{-e^{e^x}} e^{e^x+x} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right ) \, dx\\ &=3 \int \frac {2^{-e^{e^x}} e^{e^x} (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}}}{3+3 x-\log (9)} \, dx+\int 2^{1-e^{e^x}} e^{e^x} (2 x+\log (-3-3 x+\log (9)))^{-1+e^{e^x}} \, dx+\int 2^{-e^{e^x}} e^{e^x+x} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 1.11, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2^{-e^{e^x}} (2 x+\log (-3-3 x+\log (9)))^{e^{e^x}} \left (e^{e^x} (-9-6 x+2 \log (9))+e^{e^x} \left (e^x \left (-6 x-6 x^2+2 x \log (9)\right )+e^x (-3-3 x+\log (9)) \log (-3-3 x+\log (9))\right ) \log \left (\frac {1}{2} (2 x+\log (-3-3 x+\log (9)))\right )\right )}{-6 x-6 x^2+2 x \log (9)+(-3-3 x+\log (9)) \log (-3-3 x+\log (9))} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.65, size = 18, normalized size = 0.90 \begin {gather*} {\left (x + \frac {1}{2} \, \log \left (-3 \, x + 2 \, \log \relax (3) - 3\right )\right )}^{e^{\left (e^{x}\right )}} \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 {sage}_{0} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 19, normalized size = 0.95
method | result | size |
risch | \(\left (\frac {\ln \left (2 \ln \relax (3)-3 x -3\right )}{2}+x \right )^{{\mathrm e}^{{\mathrm e}^{x}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 28, normalized size = 1.40 \begin {gather*} e^{\left (-e^{\left (e^{x}\right )} \log \relax (2) + e^{\left (e^{x}\right )} \log \left (2 \, x + \log \left (-3 \, x + 2 \, \log \relax (3) - 3\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.51, size = 16, normalized size = 0.80 \begin {gather*} {\left (x+\frac {\ln \left (\ln \relax (9)-3\,x-3\right )}{2}\right )}^{{\mathrm {e}}^{{\mathrm {e}}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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