Optimal. Leaf size=32 \[ e^{e^{x \left (\frac {3}{x}-\log \left (\frac {1}{9} x \left (\frac {1}{3 x}+\log (4)\right )\right )\right )}}+x \]
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Rubi [F] time = 4.12, 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 {1+3 x \log (4)+\exp \left (3+e^{3-x \log \left (\frac {1}{27} (1+3 x \log (4))\right )}-x \log \left (\frac {1}{27} (1+3 x \log (4))\right )\right ) \left (-3 x \log (4)+(-1-3 x \log (4)) \log \left (\frac {1}{27} (1+3 x \log (4))\right )\right )}{1+3 x \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-1-x} \left (x \log (64)+\log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )+x \log (64) \log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )\right )\right ) \, dx\\ &=x-\int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-1-x} \left (x \log (64)+\log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )+x \log (64) \log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )\right ) \, dx\\ &=x-\int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-1-x} \left (x \log (64)+(1+x \log (64)) \log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )\right ) \, dx\\ &=x-\int \left (27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} x \log (64) (1+x \log (64))^{-1-x}+27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right )\right ) \, dx\\ &=x-\log (64) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} x (1+x \log (64))^{-1-x} \, dx-\int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right ) \, dx\\ &=x-\log (64) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} x (1+x \log (64))^{-1-x} \, dx-\log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right ) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \, dx+\int \frac {6 \log (2) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \, dx}{1+x \log (64)} \, dx\\ &=x+(6 \log (2)) \int \frac {\int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \, dx}{1+x \log (64)} \, dx-\log (64) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} x (1+x \log (64))^{-1-x} \, dx-\log \left (\frac {1}{27}+\frac {2}{9} x \log (2)\right ) \int 27^x e^{3+27^x e^3 (1+3 x \log (4))^{-x}} (1+x \log (64))^{-x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 6.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1+3 x \log (4)+e^{3+e^{3-x \log \left (\frac {1}{27} (1+3 x \log (4))\right )}-x \log \left (\frac {1}{27} (1+3 x \log (4))\right )} \left (-3 x \log (4)+(-1-3 x \log (4)) \log \left (\frac {1}{27} (1+3 x \log (4))\right )\right )}{1+3 x \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.97, size = 59, normalized size = 1.84 \begin {gather*} {\left (x e^{\left (-x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) + 3\right )} + e^{\left (-x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) + e^{\left (-x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) + 3\right )} + 3\right )}\right )} e^{\left (x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) - 3\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*} \int -\frac {{\left (6 \, x \log \relax (2) + {\left (6 \, x \log \relax (2) + 1\right )} \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right )\right )} e^{\left (-x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) + e^{\left (-x \log \left (\frac {2}{9} \, x \log \relax (2) + \frac {1}{27}\right ) + 3\right )} + 3\right )} - 6 \, x \log \relax (2) - 1}{6 \, x \log \relax (2) + 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 18, normalized size = 0.56
method | result | size |
default | \(x +{\mathrm e}^{{\mathrm e}^{-x \ln \left (\frac {2 x \ln \relax (2)}{9}+\frac {1}{27}\right )+3}}\) | \(18\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{-x \ln \left (\frac {2 x \ln \relax (2)}{9}+\frac {1}{27}\right )+3}}\) | \(18\) |
risch | \(x +{\mathrm e}^{\left (\frac {2 x \ln \relax (2)}{9}+\frac {1}{27}\right )^{-x} {\mathrm e}^{3}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.62, size = 61, normalized size = 1.91 \begin {gather*} \frac {1}{6} \, {\left (\frac {6 \, x}{\log \relax (2)} - \frac {\log \left (6 \, x \log \relax (2) + 1\right )}{\log \relax (2)^{2}}\right )} \log \relax (2) + \frac {\log \left (6 \, x \log \relax (2) + 1\right )}{6 \, \log \relax (2)} + e^{\left (e^{\left (3 \, x \log \relax (3) - x \log \left (6 \, x \log \relax (2) + 1\right ) + 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.22, size = 17, normalized size = 0.53 \begin {gather*} x+{\mathrm {e}}^{\frac {{\mathrm {e}}^3}{{\left (\frac {2\,x\,\ln \relax (2)}{9}+\frac {1}{27}\right )}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.18, size = 20, normalized size = 0.62 \begin {gather*} x + e^{e^{- x \log {\left (\frac {2 x \log {\relax (2 )}}{9} + \frac {1}{27} \right )} + 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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