Optimal. Leaf size=17 \[ x+e^{8/3} \left (-5+e+e^x+x+\log (4)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2194} \begin {gather*} \left (1+e^{8/3}\right ) x+e^{x+\frac {8}{3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (1+e^{8/3}\right ) x+\int e^{\frac {8}{3}+x} \, dx\\ &=e^{\frac {8}{3}+x}+\left (1+e^{8/3}\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} e^{\frac {8}{3}+x}+x+e^{8/3} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 10, normalized size = 0.59 \begin {gather*} x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 10, normalized size = 0.59 \begin {gather*} x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 11, normalized size = 0.65
method | result | size |
risch | \(x +{\mathrm e}^{\frac {8}{3}} x +{\mathrm e}^{x +\frac {8}{3}}\) | \(11\) |
derivativedivides | \({\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}+\left ({\mathrm e}^{\frac {8}{3}}+1\right ) \ln \left ({\mathrm e}^{x}\right )\) | \(15\) |
default | \(x +{\mathrm e}^{\frac {8}{3}} x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(16\) |
norman | \(\left ({\mathrm e}^{\frac {8}{3}}+1\right ) x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 10, normalized size = 0.59 \begin {gather*} x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 11, normalized size = 0.65 \begin {gather*} {\mathrm {e}}^{x+\frac {8}{3}}+x\,\left ({\mathrm {e}}^{8/3}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} x \left (1 + e^{\frac {8}{3}}\right ) + e^{\frac {8}{3}} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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