Optimal. Leaf size=29 \[ -3-2 x+\log \left (\frac {x^2}{1-4 x-\frac {2 x}{3-e^5}}\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 28, normalized size of antiderivative = 0.97, number of steps used = 4, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {1984, 1593, 893} \begin {gather*} -2 x+2 \log (x)-\log \left (-2 \left (7-2 e^5\right ) x-e^5+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 893
Rule 1593
Rule 1984
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (3-e^5\right )-2 \left (10-3 e^5\right ) x+4 \left (7-2 e^5\right ) x^2}{\left (3-e^5\right ) x-2 \left (7-2 e^5\right ) x^2} \, dx\\ &=\int \frac {2 \left (3-e^5\right )-2 \left (10-3 e^5\right ) x+4 \left (7-2 e^5\right ) x^2}{x \left (3-e^5-2 \left (7-2 e^5\right ) x\right )} \, dx\\ &=\int \left (-2+\frac {2}{x}+\frac {2 \left (7-2 e^5\right )}{3-e^5-2 \left (7-2 e^5\right ) x}\right ) \, dx\\ &=-2 x+2 \log (x)-\log \left (3-e^5-2 \left (7-2 e^5\right ) x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 27, normalized size = 0.93 \begin {gather*} -2 x+2 \log (x)-\log \left (3-e^5-14 x+4 e^5 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 24, normalized size = 0.83 \begin {gather*} -2 \, x - \log \left ({\left (4 \, x - 1\right )} e^{5} - 14 \, x + 3\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 43, normalized size = 1.48 \begin {gather*} -\frac {2 \, {\left (2 \, x e^{5} - 7 \, x\right )}}{2 \, e^{5} - 7} - \log \left ({\left | 4 \, x e^{5} - 14 \, x - e^{5} + 3 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 26, normalized size = 0.90
method | result | size |
norman | \(-2 x +2 \ln \relax (x )-\ln \left (4 x \,{\mathrm e}^{5}-{\mathrm e}^{5}-14 x +3\right )\) | \(26\) |
risch | \(-2 x -\ln \left (x \left (4 \,{\mathrm e}^{5}-14\right )+3-{\mathrm e}^{5}\right )+2 \ln \left (-x \right )\) | \(28\) |
default | \(-2 x +2 \ln \relax (x )+\frac {2 \left (-2 \,{\mathrm e}^{5}+7\right ) \ln \left (4 x \,{\mathrm e}^{5}-{\mathrm e}^{5}-14 x +3\right )}{4 \,{\mathrm e}^{5}-14}\) | \(40\) |
meijerg | \(\frac {\left (-8 \,{\mathrm e}^{5}+28\right ) \left ({\mathrm e}^{5}-3\right )^{2} \left (\frac {2 x \left (2 \,{\mathrm e}^{5}-7\right )}{3-{\mathrm e}^{5}}-\ln \left (1+\frac {2 x \left (2 \,{\mathrm e}^{5}-7\right )}{3-{\mathrm e}^{5}}\right )\right )}{4 \left (3-{\mathrm e}^{5}\right ) \left (2 \,{\mathrm e}^{5}-7\right )^{2}}-\frac {\left (6 \,{\mathrm e}^{5}-20\right ) \left ({\mathrm e}^{5}-3\right ) \ln \left (1+\frac {2 x \left (2 \,{\mathrm e}^{5}-7\right )}{3-{\mathrm e}^{5}}\right )}{2 \left (3-{\mathrm e}^{5}\right ) \left (2 \,{\mathrm e}^{5}-7\right )}+\frac {2 \,{\mathrm e}^{5} \left ({\mathrm e}^{5}-3\right ) \left (\ln \relax (x )+\ln \relax (2)+\ln \left (2 \,{\mathrm e}^{5}-7\right )+\ln \left (-\frac {1}{3-{\mathrm e}^{5}}\right )+i \pi -\ln \left (1+\frac {2 x \left (2 \,{\mathrm e}^{5}-7\right )}{3-{\mathrm e}^{5}}\right )\right )}{\left (3-{\mathrm e}^{5}\right )^{2}}-\frac {6 \left ({\mathrm e}^{5}-3\right ) \left (\ln \relax (x )+\ln \relax (2)+\ln \left (2 \,{\mathrm e}^{5}-7\right )+\ln \left (-\frac {1}{3-{\mathrm e}^{5}}\right )+i \pi -\ln \left (1+\frac {2 x \left (2 \,{\mathrm e}^{5}-7\right )}{3-{\mathrm e}^{5}}\right )\right )}{\left (3-{\mathrm e}^{5}\right )^{2}}\) | \(248\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 26, normalized size = 0.90 \begin {gather*} -2 \, x - \log \left (2 \, x {\left (2 \, e^{5} - 7\right )} - e^{5} + 3\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.07, size = 46, normalized size = 1.59 \begin {gather*} 2\,\ln \relax (x)-\ln \left (12\,x\,{\mathrm {e}}^5-3\,{\mathrm {e}}^5-42\,x+9\right )+\frac {28\,x}{4\,{\mathrm {e}}^5-14}-\frac {8\,x\,{\mathrm {e}}^5}{4\,{\mathrm {e}}^5-14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.85, size = 24, normalized size = 0.83 \begin {gather*} - 2 x + 2 \log {\relax (x )} - \log {\left (x + \frac {9 - 3 e^{5}}{-42 + 12 e^{5}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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