Optimal. Leaf size=23 \[ -\frac {7}{\log \left (x \left (e-x+x^2-\log (4-2 x)\right )\right )} \]
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Rubi [A] time = 0.17, antiderivative size = 26, normalized size of antiderivative = 1.13, number of steps used = 1, number of rules used = 1, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6686} \begin {gather*} -\frac {7}{\log \left (x^3-x^2+e x-x \log (4-2 x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {7}{\log \left (e x-x^2+x^3-x \log (4-2 x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 22, normalized size = 0.96 \begin {gather*} -\frac {7}{\log (x (e+(-1+x) x-\log (4-2 x)))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 27, normalized size = 1.17 \begin {gather*} -\frac {7}{\log \left (x^{3} - x^{2} + x e - x \log \left (-2 \, x + 4\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 27, normalized size = 1.17 \begin {gather*} -\frac {7}{\log \left (x^{3} - x^{2} + x e - x \log \left (-2 \, x + 4\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.13, size = 189, normalized size = 8.22
method | result | size |
risch | \(\frac {14 i}{\pi \,\mathrm {csgn}\left (i \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right ) \mathrm {csgn}\left (i x \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right ) \mathrm {csgn}\left (i x \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right ) \mathrm {csgn}\left (i x \right )-\pi \mathrm {csgn}\left (i x \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right )^{3}+\pi \mathrm {csgn}\left (i x \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )\right )^{2} \mathrm {csgn}\left (i x \right )-2 i \ln \relax (x )-2 i \ln \left (x^{2}+{\mathrm e}-\ln \left (4-2 x \right )-x \right )}\) | \(189\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.51, size = 30, normalized size = 1.30 \begin {gather*} -\frac {7}{\log \left (-i \, \pi + x^{2} - x + e - \log \relax (2) - \log \left (x - 2\right )\right ) + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.09, size = 27, normalized size = 1.17 \begin {gather*} -\frac {7}{\ln \left (x\,\mathrm {e}-x\,\ln \left (4-2\,x\right )-x^2+x^3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.46, size = 24, normalized size = 1.04 \begin {gather*} - \frac {7}{\log {\left (x^{3} - x^{2} - x \log {\left (4 - 2 x \right )} + e x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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