Optimal. Leaf size=13 \[ \frac {\log (3)}{3+e^x-2 x} \]
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Rubi [A] time = 0.10, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6688, 12, 6686} \begin {gather*} \frac {\log (3)}{-2 x+e^x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (2-e^x\right ) \log (3)}{\left (3+e^x-2 x\right )^2} \, dx\\ &=\log (3) \int \frac {2-e^x}{\left (3+e^x-2 x\right )^2} \, dx\\ &=\frac {\log (3)}{3+e^x-2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {\log (3)}{3+e^x-2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.42, size = 15, normalized size = 1.15 \begin {gather*} -\frac {\log \relax (3)}{2 \, x - e^{x} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 1.15 \begin {gather*} -\frac {\log \relax (3)}{2 \, x - e^{x} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 16, normalized size = 1.23
method | result | size |
norman | \(-\frac {\ln \relax (3)}{2 x -3-{\mathrm e}^{x}}\) | \(16\) |
risch | \(-\frac {\ln \relax (3)}{2 x -3-{\mathrm e}^{x}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 15, normalized size = 1.15 \begin {gather*} -\frac {\log \relax (3)}{2 \, x - e^{x} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.28, size = 12, normalized size = 0.92 \begin {gather*} \frac {\ln \relax (3)}{{\mathrm {e}}^x-2\,x+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.77 \begin {gather*} \frac {\log {\relax (3 )}}{- 2 x + e^{x} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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