Optimal. Leaf size=20 \[ 5+e^{e^{e^{4+x}}+x}-x (-2+\log (4)) \]
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Rubi [A] time = 0.08, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2282, 2288} \begin {gather*} e^{x+e^{e^{x+4}}}+x (2-\log (4)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2282
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x (2-\log (4))+\int e^{e^{e^{4+x}}+x} \left (1+e^{4+e^{4+x}+x}\right ) \, dx\\ &=x (2-\log (4))+\operatorname {Subst}\left (\int e^{e^{e^4 x}} \left (1+e^{4+e^4 x} x\right ) \, dx,x,e^x\right )\\ &=e^{e^{e^{4+x}}+x}+x (2-\log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 20, normalized size = 1.00 \begin {gather*} e^{e^{e^{4+x}}+x}+2 x-x \log (4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 32, normalized size = 1.60 \begin {gather*} -2 \, x \log \relax (2) + 2 \, x + e^{\left ({\left (x e^{\left (x + 4\right )} + e^{\left (x + e^{\left (x + 4\right )} + 4\right )}\right )} e^{\left (-x - 4\right )}\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 {\left (e^{\left (x + e^{\left (x + 4\right )} + 4\right )} + 1\right )} e^{\left (x + e^{\left (e^{\left (x + 4\right )}\right )}\right )} - 2 \, \log \relax (2) + 2\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.90
method | result | size |
default | \(2 x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4+x}}+x}-2 x \ln \relax (2)\) | \(18\) |
norman | \(\left (2-2 \ln \relax (2)\right ) x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4+x}}+x}\) | \(18\) |
risch | \(2 x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{4+x}}+x}-2 x \ln \relax (2)\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 17, normalized size = 0.85 \begin {gather*} -2 \, x \log \relax (2) + 2 \, x + e^{\left (x + e^{\left (e^{\left (x + 4\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.16, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{x+{\mathrm {e}}^{{\mathrm {e}}^4\,{\mathrm {e}}^x}}-x\,\left (\ln \relax (4)-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 17, normalized size = 0.85 \begin {gather*} x \left (2 - 2 \log {\relax (2 )}\right ) + e^{x + e^{e^{x + 4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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