Optimal. Leaf size=29 \[ 2 \log \left (\frac {3 \left (-\frac {2-\frac {1}{x}}{x}+x\right )}{x (e+5 x)}\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 34, normalized size of antiderivative = 1.17, number of steps used = 3, number of rules used = 2, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2074, 628} \begin {gather*} 2 \log \left (-x^2-x+1\right )+2 \log (1-x)-6 \log (x)-2 \log (5 x+e) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2}{-1+x}-\frac {6}{x}-\frac {10}{e+5 x}+\frac {2 (1+2 x)}{-1+x+x^2}\right ) \, dx\\ &=2 \log (1-x)-6 \log (x)-2 \log (e+5 x)+2 \int \frac {1+2 x}{-1+x+x^2} \, dx\\ &=2 \log (1-x)-6 \log (x)-2 \log (e+5 x)+2 \log \left (1-x-x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 24, normalized size = 0.83 \begin {gather*} -6 \log (x)-2 \log (e+5 x)+2 \log \left (1-2 x+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 25, normalized size = 0.86 \begin {gather*} 2 \, \log \left (x^{3} - 2 \, x + 1\right ) - 2 \, \log \left (5 \, x + e\right ) - 6 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 33, normalized size = 1.14 \begin {gather*} 2 \, \log \left ({\left | x^{2} + x - 1 \right |}\right ) - 2 \, \log \left ({\left | 5 \, x + e \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) - 6 \, \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 = 0.08, size = 30, normalized size = 1.03
method | result | size |
default | \(2 \ln \left (x -1\right )-6 \ln \relax (x )+2 \ln \left (x^{2}+x -1\right )-2 \ln \left (5 x +{\mathrm e}\right )\) | \(30\) |
norman | \(2 \ln \left (x -1\right )-6 \ln \relax (x )+2 \ln \left (x^{2}+x -1\right )-2 \ln \left (5 x +{\mathrm e}\right )\) | \(30\) |
risch | \(-2 \ln \left (-{\mathrm e}-5 x \right )-6 \ln \relax (x )+2 \ln \left (-x^{3}+2 x -1\right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 29, normalized size = 1.00 \begin {gather*} 2 \, \log \left (x^{2} + x - 1\right ) - 2 \, \log \left (5 \, x + e\right ) + 2 \, \log \left (x - 1\right ) - 6 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.85, size = 25, normalized size = 0.86 \begin {gather*} 2\,\ln \left (x^3-2\,x+1\right )-2\,\ln \left (x+\frac {\mathrm {e}}{5}\right )-6\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 9.40, size = 26, normalized size = 0.90 \begin {gather*} - 6 \log {\relax (x )} - 2 \log {\left (x + \frac {e}{5} \right )} + 2 \log {\left (x^{3} - 2 x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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