Optimal. Leaf size=19 \[ e^x+e^{x \left (-10+\frac {7 x}{4}+\log (2 x)\right )} \]
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Rubi [A] time = 0.10, antiderivative size = 26, normalized size of antiderivative = 1.37, number of steps used = 4, number of rules used = 3, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {12, 2194, 6706} \begin {gather*} 2^x e^{\frac {1}{4} \left (7 x^2-40 x\right )} x^x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (2 e^x+e^{\frac {1}{4} \left (-40 x+7 x^2+4 x \log (2 x)\right )} (-18+7 x+2 \log (2 x))\right ) \, dx\\ &=\frac {1}{2} \int e^{\frac {1}{4} \left (-40 x+7 x^2+4 x \log (2 x)\right )} (-18+7 x+2 \log (2 x)) \, dx+\int e^x \, dx\\ &=e^x+2^x e^{\frac {1}{4} \left (-40 x+7 x^2\right )} x^x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.46, size = 24, normalized size = 1.26 \begin {gather*} e^x+2^x e^{-10 x+\frac {7 x^2}{4}} x^x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {7}{4} \, x^{2} + x \log \left (2 \, x\right ) - 10 \, x\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {7}{4} \, x^{2} + x \log \left (2 \, x\right ) - 10 \, x\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 19, normalized size = 1.00
method | result | size |
risch | \(\left (2 x \right )^{x} {\mathrm e}^{\frac {x \left (7 x -40\right )}{4}}+{\mathrm e}^{x}\) | \(19\) |
default | \({\mathrm e}^{x \ln \left (2 x \right )+\frac {7 x^{2}}{4}-10 x}+{\mathrm e}^{x}\) | \(20\) |
norman | \({\mathrm e}^{x \ln \left (2 x \right )+\frac {7 x^{2}}{4}-10 x}+{\mathrm e}^{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {7}{4} \, x^{2} + x \log \left (2 \, x\right ) - 10 \, x\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.34, size = 19, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^x+{\mathrm {e}}^{\frac {7\,x^2}{4}-10\,x}\,{\left (2\,x\right )}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.38, size = 20, normalized size = 1.05 \begin {gather*} e^{x} + e^{\frac {7 x^{2}}{4} + x \log {\left (2 x \right )} - 10 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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