Optimal. Leaf size=15 \[ -\frac {4 \log \left (e^{2+x}-2 x\right )}{e^2} \]
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Rubi [A] time = 0.04, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6684} \begin {gather*} -\frac {4 \log \left (e^{x+2}-2 x\right )}{e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {4 \log \left (e^{2+x}-2 x\right )}{e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 15, normalized size = 1.00 \begin {gather*} -\frac {4 \log \left (e^{2+x}-2 x\right )}{e^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 15, normalized size = 1.00 \begin {gather*} -4 \, e^{\left (-2\right )} \log \left (-2 \, x e^{2} + e^{\left (x + 4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 15, normalized size = 1.00 \begin {gather*} -4 \, e^{\left (-2\right )} \log \left (2 \, x - e^{\left (x + 2\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 18, normalized size = 1.20
method | result | size |
norman | \(-4 \,{\mathrm e}^{-2} \ln \left (2 x -{\mathrm e}^{2+x}\right )\) | \(18\) |
risch | \(8 \,{\mathrm e}^{-2}-4 \ln \left ({\mathrm e}^{2+x}-2 x \right ) {\mathrm e}^{-2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 1.13 \begin {gather*} -4 \, e^{\left (-2\right )} \log \left (2 \, x e^{2} - e^{\left (x + 4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.46, size = 15, normalized size = 1.00 \begin {gather*} -4\,\ln \left (2\,x-{\mathrm {e}}^{x+2}\right )\,{\mathrm {e}}^{-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 1.00 \begin {gather*} - \frac {4 \log {\left (- 2 x + e^{x + 2} \right )}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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