Optimal. Leaf size=20 \[ 1+e^{x/2}-e^{e^{\log ^2(10)}} x \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 2194} \begin {gather*} e^{x/2}-x e^{e^{\log ^2(10)}} \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^{e^{\log ^2(10)}}+e^{x/2}\right ) \, dx\\ &=-e^{e^{\log ^2(10)}} x+\frac {1}{2} \int e^{x/2} \, dx\\ &=e^{x/2}-e^{e^{\log ^2(10)}} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.25 \begin {gather*} \frac {1}{2} \left (2 e^{x/2}-2 e^{e^{\log ^2(10)}} x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 14, normalized size = 0.70 \begin {gather*} -x e^{\left (e^{\left (\log \left (10\right )^{2}\right )}\right )} + e^{\left (\frac {1}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 14, normalized size = 0.70 \begin {gather*} -x e^{\left (e^{\left (\log \left (10\right )^{2}\right )}\right )} + e^{\left (\frac {1}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 0.75
method | result | size |
default | \({\mathrm e}^{\frac {x}{2}}-x \,{\mathrm e}^{{\mathrm e}^{\ln \left (10\right )^{2}}}\) | \(15\) |
norman | \({\mathrm e}^{\frac {x}{2}}-x \,{\mathrm e}^{{\mathrm e}^{\ln \left (10\right )^{2}}}\) | \(15\) |
risch | \(-{\mathrm e}^{{\mathrm e}^{\left (\ln \relax (2)+\ln \relax (5)\right )^{2}}} x +{\mathrm e}^{\frac {x}{2}}\) | \(18\) |
derivativedivides | \({\mathrm e}^{\frac {x}{2}}-2 \,{\mathrm e}^{{\mathrm e}^{\ln \left (10\right )^{2}}} \ln \left ({\mathrm e}^{\frac {x}{2}}\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 14, normalized size = 0.70 \begin {gather*} -x e^{\left (e^{\left (\log \left (10\right )^{2}\right )}\right )} + e^{\left (\frac {1}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 14, normalized size = 0.70 \begin {gather*} {\mathrm {e}}^{x/2}-x\,{\mathrm {e}}^{{\mathrm {e}}^{{\ln \left (10\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.70 \begin {gather*} - x e^{e^{\log {\left (10 \right )}^{2}}} + e^{\frac {x}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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