Optimal. Leaf size=14 \[ 4+\frac {1}{4} e^{9+e^x} x \]
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Rubi [A] time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2288} \begin {gather*} \frac {1}{4} e^{e^x+9} x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{9+e^x} \left (1+e^x x\right ) \, dx\\ &=\frac {1}{4} e^{9+e^x} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{4} e^{9+e^x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 8, normalized size = 0.57 \begin {gather*} \frac {1}{4} \, x e^{\left (e^{x} + 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 8, normalized size = 0.57 \begin {gather*} \frac {1}{4} \, x e^{\left (e^{x} + 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.64
method | result | size |
norman | \(\frac {{\mathrm e}^{9+{\mathrm e}^{x}} x}{4}\) | \(9\) |
risch | \(\frac {{\mathrm e}^{9+{\mathrm e}^{x}} x}{4}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{4} \, {\rm Ei}\left (e^{x}\right ) e^{9} + \frac {1}{4} \, x e^{\left (e^{x} + 9\right )} - \frac {1}{4} \, \int e^{\left (e^{x} + 9\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.39, size = 8, normalized size = 0.57 \begin {gather*} \frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^9}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 8, normalized size = 0.57 \begin {gather*} \frac {x e^{e^{x} + 9}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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