Optimal. Leaf size=12 \[ e^4+\frac {e^x}{2}+x \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} x+\frac {e^x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (2+e^x\right ) \, dx\\ &=x+\frac {\int e^x \, dx}{2}\\ &=\frac {e^x}{2}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} \frac {1}{2} \left (e^x+2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 6, normalized size = 0.50 \begin {gather*} x + \frac {1}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 6, normalized size = 0.50 \begin {gather*} x + \frac {1}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.58
method | result | size |
default | \(x +\frac {{\mathrm e}^{x}}{2}\) | \(7\) |
norman | \(x +\frac {{\mathrm e}^{x}}{2}\) | \(7\) |
risch | \(x +\frac {{\mathrm e}^{x}}{2}\) | \(7\) |
derivativedivides | \(\frac {{\mathrm e}^{x}}{2}+\ln \left ({\mathrm e}^{x}\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 6, normalized size = 0.50 \begin {gather*} x + \frac {1}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 6, normalized size = 0.50 \begin {gather*} x+\frac {{\mathrm {e}}^x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.42 \begin {gather*} x + \frac {e^{x}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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