Optimal. Leaf size=28 \[ x-\log \left (3+e^{-5+e^{\frac {1}{4} (1-x-x (3+x))}}\right ) \]
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Rubi [A] time = 0.79, antiderivative size = 29, normalized size of antiderivative = 1.04, number of steps used = 3, number of rules used = 2, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6742, 6684} \begin {gather*} x-\log \left (e^{e^{-\frac {x^2}{4}-x+\frac {1}{4}}}+3 e^5\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {e^{\frac {1}{4}+e^{\frac {1}{4}-x-\frac {x^2}{4}}-x-\frac {x^2}{4}} (2+x)}{2 \left (3 e^5+e^{e^{\frac {1}{4}-x-\frac {x^2}{4}}}\right )}\right ) \, dx\\ &=x+\frac {1}{2} \int \frac {e^{\frac {1}{4}+e^{\frac {1}{4}-x-\frac {x^2}{4}}-x-\frac {x^2}{4}} (2+x)}{3 e^5+e^{e^{\frac {1}{4}-x-\frac {x^2}{4}}}} \, dx\\ &=x-\log \left (3 e^5+e^{e^{\frac {1}{4}-x-\frac {x^2}{4}}}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.70, size = 29, normalized size = 1.04 \begin {gather*} x-\log \left (3 e^5+e^{e^{\frac {1}{4}-x-\frac {x^2}{4}}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 21, normalized size = 0.75 \begin {gather*} x - \log \left (e^{\left (e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )} - 5\right )} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.55, size = 87, normalized size = 3.11 \begin {gather*} -\frac {1}{4} \, x^{2} e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )} - \frac {1}{4} \, x^{2} - x e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )} - e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )} - \log \left (e^{\left (-\frac {1}{4} \, x^{2} - x + e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )}\right )} + 3 \, e^{\left (-\frac {1}{4} \, x^{2} - x + 5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 23, normalized size = 0.82
method | result | size |
risch | \(x -5-\ln \left ({\mathrm e}^{{\mathrm e}^{-\frac {1}{4} x^{2}-x +\frac {1}{4}}-5}+3\right )\) | \(23\) |
norman | \(x -\ln \left (2 \,{\mathrm e}^{{\mathrm e}^{-\frac {1}{4} x^{2}-x +\frac {1}{4}}-5}+6\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.76, size = 22, normalized size = 0.79 \begin {gather*} x - \log \left (3 \, e^{5} + e^{\left (e^{\left (-\frac {1}{4} \, x^{2} - x + \frac {1}{4}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 24, normalized size = 0.86 \begin {gather*} x-\ln \left ({\mathrm {e}}^{{\mathrm {e}}^{-x}\,{\mathrm {e}}^{1/4}\,{\mathrm {e}}^{-\frac {x^2}{4}}}\,{\mathrm {e}}^{-5}+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 34, normalized size = 1.21 \begin {gather*} x - \frac {e^{- \frac {x^{2}}{4} - x + \frac {1}{4}}}{2} - \frac {\log {\left (e^{e^{- \frac {x^{2}}{4} - x + \frac {1}{4}} - 5} + 3 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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