Optimal. Leaf size=18 \[ 260+e^{4 e^{e^{e^x}}}+x-\log (4) \]
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Rubi [A] time = 0.05, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 5, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2282, 2194} \begin {gather*} x+e^{4 e^{e^{e^x}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+4 \int e^{4 e^{e^{e^x}}+e^{e^x}+e^x+x} \, dx\\ &=x+4 \operatorname {Subst}\left (\int e^{4 e^{e^x}+e^x+x} \, dx,x,e^x\right )\\ &=x+4 \operatorname {Subst}\left (\int e^{4 e^x+x} \, dx,x,e^{e^x}\right )\\ &=x+4 \operatorname {Subst}\left (\int e^{4 x} \, dx,x,e^{e^{e^x}}\right )\\ &=e^{4 e^{e^{e^x}}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 13, normalized size = 0.72 \begin {gather*} e^{4 e^{e^{e^x}}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.71, size = 40, normalized size = 2.22 \begin {gather*} {\left (x e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + e^{\left (x + e^{x} + e^{\left (e^{x}\right )} + 4 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )}\right )} e^{\left (-x - e^{x} - e^{\left (e^{x}\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 4 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )} + 4 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 1\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 10, normalized size = 0.56
method | result | size |
default | \(x +{\mathrm e}^{4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}\) | \(10\) |
norman | \(x +{\mathrm e}^{4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}\) | \(10\) |
risch | \(x +{\mathrm e}^{4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}\) | \(10\) |
derivativedivides | \(\ln \left ({\mathrm e}^{x}\right )+{\mathrm e}^{4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 9, normalized size = 0.50 \begin {gather*} x + e^{\left (4 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 9, normalized size = 0.50 \begin {gather*} x+{\mathrm {e}}^{4\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 10, normalized size = 0.56 \begin {gather*} x + e^{4 e^{e^{e^{x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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