Optimal. Leaf size=19 \[ 1-2 e^{-4 (2-x)} (3-\log (x)) \]
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Rubi [A] time = 0.05, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2288} \begin {gather*} -\frac {2 e^{4 x-8} (3 x-x \log (x))}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {2 e^{-8+4 x} (3 x-x \log (x))}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.68 \begin {gather*} 2 e^{-8+4 x} (-3+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.67, size = 19, normalized size = 1.00 \begin {gather*} 2 \, e^{\left (4 \, x - 8\right )} \log \relax (x) - 6 \, e^{\left (4 \, x - 8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 18, normalized size = 0.95 \begin {gather*} 2 \, {\left (e^{\left (4 \, x\right )} \log \relax (x) - 3 \, e^{\left (4 \, x\right )}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.84
method | result | size |
norman | \(\left (2 \ln \relax (x )-6\right ) {\mathrm e}^{4 x -8}\) | \(16\) |
risch | \(2 \ln \relax (x ) {\mathrm e}^{4 x -8}-6 \,{\mathrm e}^{4 x -8}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 19, normalized size = 1.00 \begin {gather*} 2 \, e^{\left (4 \, x - 8\right )} \log \relax (x) - 6 \, e^{\left (4 \, x - 8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.86, size = 13, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{4\,x-8}\,\left (2\,\ln \relax (x)-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 12, normalized size = 0.63 \begin {gather*} \left (2 \log {\relax (x )} - 6\right ) e^{4 x - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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