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 = 4.46, 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 = 4.61, 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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Maple [A]
time = 1.06, size = 18, normalized size = 0.56
method | result | size |
default | \(x +{\mathrm e}^{{\mathrm e}^{-x \ln \left (\frac {2 x \ln \left (2\right )}{9}+\frac {1}{27}\right )+3}}\) | \(18\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{-x \ln \left (\frac {2 x \ln \left (2\right )}{9}+\frac {1}{27}\right )+3}}\) | \(18\) |
risch | \(x +{\mathrm e}^{\left (\frac {2 x \ln \left (2\right )}{9}+\frac {1}{27}\right )^{-x} {\mathrm e}^{3}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 61 vs.
\(2 (26) = 52\).
time = 0.63, size = 61, normalized size = 1.91 \begin {gather*} \frac {1}{6} \, {\left (\frac {6 \, x}{\log \left (2\right )} - \frac {\log \left (6 \, x \log \left (2\right ) + 1\right )}{\log \left (2\right )^{2}}\right )} \log \left (2\right ) + \frac {\log \left (6 \, x \log \left (2\right ) + 1\right )}{6 \, \log \left (2\right )} + e^{\left (e^{\left (3 \, x \log \left (3\right ) - x \log \left (6 \, x \log \left (2\right ) + 1\right ) + 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 59 vs.
\(2 (26) = 52\).
time = 0.39, size = 59, normalized size = 1.84 \begin {gather*} {\left (x e^{\left (-x \log \left (\frac {2}{9} \, x \log \left (2\right ) + \frac {1}{27}\right ) + 3\right )} + e^{\left (-x \log \left (\frac {2}{9} \, x \log \left (2\right ) + \frac {1}{27}\right ) + e^{\left (-x \log \left (\frac {2}{9} \, x \log \left (2\right ) + \frac {1}{27}\right ) + 3\right )} + 3\right )}\right )} e^{\left (x \log \left (\frac {2}{9} \, x \log \left (2\right ) + \frac {1}{27}\right ) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.45, size = 20, normalized size = 0.62 \begin {gather*} x + e^{e^{- x \log {\left (\frac {2 x \log {\left (2 \right )}}{9} + \frac {1}{27} \right )} + 3}} \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 = 4.22, size = 17, normalized size = 0.53 \begin {gather*} x+{\mathrm {e}}^{\frac {{\mathrm {e}}^3}{{\left (\frac {2\,x\,\ln \left (2\right )}{9}+\frac {1}{27}\right )}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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