Optimal. Leaf size=20 \[ 5 \left (-2+e^{e^x}+\frac {1}{5} \left (4+(3+x)^2\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.70, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2282, 2194} \begin {gather*} x^2+6 x+5 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} &=6 x+x^2+5 \int e^{e^x+x} \, dx\\ &=6 x+x^2+5 \operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=5 e^{e^x}+6 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.70 \begin {gather*} 5 e^{e^x}+6 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 23, normalized size = 1.15 \begin {gather*} {\left ({\left (x^{2} + 6 \, x\right )} e^{x} + 5 \, e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 12, normalized size = 0.60 \begin {gather*} x^{2} + 6 \, x + 5 \, e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.65
method | result | size |
default | \(x^{2}+6 x +5 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(13\) |
norman | \(x^{2}+6 x +5 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(13\) |
risch | \(x^{2}+6 x +5 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 12, normalized size = 0.60 \begin {gather*} x^{2} + 6 \, x + 5 \, e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 12, normalized size = 0.60 \begin {gather*} 6\,x+5\,{\mathrm {e}}^{{\mathrm {e}}^x}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.60 \begin {gather*} x^{2} + 6 x + 5 e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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