Optimal. Leaf size=22 \[ 4+e^{x/2}+x+e^4 \left (2+x \log \left (\frac {9}{4}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 0.91, 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 \left (1+e^4 \log \left (\frac {9}{4}\right )\right ) \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/2}+2 e^4 \log \left (\frac {9}{4}\right )\right ) \, dx\\ &=x \left (1+e^4 \log \left (\frac {9}{4}\right )\right )+\frac {1}{2} \int e^{x/2} \, dx\\ &=e^{x/2}+x \left (1+e^4 \log \left (\frac {9}{4}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.82 \begin {gather*} e^{x/2}+x+e^4 x \log \left (\frac {9}{4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 13, normalized size = 0.59 \begin {gather*} -x e^{4} \log \left (\frac {4}{9}\right ) + x + 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 = 0.29, size = 13, normalized size = 0.59 \begin {gather*} -x e^{4} \log \left (\frac {4}{9}\right ) + x + 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 = 14, normalized size = 0.64
method | result | size |
default | \(x -{\mathrm e}^{4} \ln \left (\frac {4}{9}\right ) x +{\mathrm e}^{\frac {x}{2}}\) | \(14\) |
derivativedivides | \({\mathrm e}^{\frac {x}{2}}+\left (-2 \,{\mathrm e}^{4} \ln \left (\frac {4}{9}\right )+2\right ) \ln \left ({\mathrm e}^{\frac {x}{2}}\right )\) | \(20\) |
risch | \(-2 x \,{\mathrm e}^{4} \ln \relax (2)+2 \,{\mathrm e}^{4} x \ln \relax (3)+{\mathrm e}^{\frac {x}{2}}+x\) | \(21\) |
norman | \(\left (-2 \,{\mathrm e}^{4} \ln \relax (2)+2 \,{\mathrm e}^{4} \ln \relax (3)+1\right ) x +{\mathrm e}^{\frac {x}{2}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 13, normalized size = 0.59 \begin {gather*} -x e^{4} \log \left (\frac {4}{9}\right ) + x + 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 = 0.08, size = 15, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{x/2}-x\,\left ({\mathrm {e}}^4\,\ln \left (\frac {4}{9}\right )-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 24, normalized size = 1.09 \begin {gather*} x \left (- 2 e^{4} \log {\relax (2 )} + 1 + 2 e^{4} \log {\relax (3 )}\right ) + e^{\frac {x}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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