Optimal. Leaf size=33 \[ -\log (x)+\log \left (\frac {1}{3} (-2+x) \left (1-x+\frac {1}{x \left (x-5 x^2\right )}\right )^2\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 37, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {2074, 1587} \begin {gather*} 2 \log \left (5 x^4-6 x^3+x^2+1\right )-2 \log (1-5 x)+\log (2-x)-5 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{-2+x}-\frac {5}{x}-\frac {10}{-1+5 x}+\frac {4 x \left (1-9 x+10 x^2\right )}{1+x^2-6 x^3+5 x^4}\right ) \, dx\\ &=-2 \log (1-5 x)+\log (2-x)-5 \log (x)+4 \int \frac {x \left (1-9 x+10 x^2\right )}{1+x^2-6 x^3+5 x^4} \, dx\\ &=-2 \log (1-5 x)+\log (2-x)-5 \log (x)+2 \log \left (1+x^2-6 x^3+5 x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 1.30 \begin {gather*} 2 \left (-\log (1-5 x)+\frac {1}{2} \log (2-x)-\frac {5 \log (x)}{2}+\log \left (1+x^2-6 x^3+5 x^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 35, normalized size = 1.06 \begin {gather*} 2 \, \log \left (5 \, x^{4} - 6 \, x^{3} + x^{2} + 1\right ) - 2 \, \log \left (5 \, x - 1\right ) + \log \left (x - 2\right ) - 5 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 38, normalized size = 1.15 \begin {gather*} 2 \, \log \left (5 \, x^{4} - 6 \, x^{3} + x^{2} + 1\right ) - 2 \, \log \left ({\left | 5 \, x - 1 \right |}\right ) + \log \left ({\left | x - 2 \right |}\right ) - 5 \, \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 = 0.06, size = 36, normalized size = 1.09
method | result | size |
default | \(-5 \ln \relax (x )+\ln \left (x -2\right )-2 \ln \left (5 x -1\right )+2 \ln \left (5 x^{4}-6 x^{3}+x^{2}+1\right )\) | \(36\) |
norman | \(-5 \ln \relax (x )+\ln \left (x -2\right )-2 \ln \left (5 x -1\right )+2 \ln \left (5 x^{4}-6 x^{3}+x^{2}+1\right )\) | \(36\) |
risch | \(-5 \ln \relax (x )+\ln \left (x -2\right )-2 \ln \left (5 x -1\right )+2 \ln \left (5 x^{4}-6 x^{3}+x^{2}+1\right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 35, normalized size = 1.06 \begin {gather*} 2 \, \log \left (5 \, x^{4} - 6 \, x^{3} + x^{2} + 1\right ) - 2 \, \log \left (5 \, x - 1\right ) + \log \left (x - 2\right ) - 5 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 33, normalized size = 1.00 \begin {gather*} 2\,\ln \left (5\,x^4-6\,x^3+x^2+1\right )+\ln \left (x-2\right )-2\,\ln \left (x-\frac {1}{5}\right )-5\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 36, normalized size = 1.09 \begin {gather*} - 5 \log {\relax (x )} + \log {\left (x - 2 \right )} - 2 \log {\left (x - \frac {1}{5} \right )} + 2 \log {\left (5 x^{4} - 6 x^{3} + x^{2} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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