Optimal. Leaf size=17 \[ \frac {e^{2-2 x}}{2 \log (e+x)} \]
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Rubi [A]
time = 0.09, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2326}
\begin {gather*} \frac {e^{2-2 x}}{2 \log (x+e)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{2-2 x}}{2 \log (e+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {e^{2-2 x}}{2 \log (e+x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 16, normalized size = 0.94
method | result | size |
norman | \(\frac {{\mathrm e}^{2} {\mathrm e}^{-2 x}}{2 \ln \left (x +{\mathrm e}\right )}\) | \(16\) |
risch | \(\frac {{\mathrm e}^{-2 x +2}}{2 \ln \left (x +{\mathrm e}\right )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 15, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-2 \, x + 2\right )}}{2 \, \log \left (x + e\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-2 \, x + 2\right )}}{2 \, \log \left (x + e\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.88 \begin {gather*} \frac {e^{2} e^{- 2 x}}{2 \log {\left (x + e \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-2 \, x + 2\right )}}{2 \, \log \left (x + e\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.92, size = 15, normalized size = 0.88 \begin {gather*} \frac {{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}{2\,\ln \left (x+\mathrm {e}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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