Optimal. Leaf size=46 \[ -\frac {1}{2 x^2}+\frac {1}{2 (1-x)}-\frac {1}{x}-\frac {7}{4} \log (1-x)+2 \log (x)-\frac {1}{4} \log (x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2058} \[ -\frac {1}{2 x^2}+\frac {1}{2 (1-x)}-\frac {1}{x}-\frac {7}{4} \log (1-x)+2 \log (x)-\frac {1}{4} \log (x+1) \]
Antiderivative was successfully verified.
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Rule 2058
Rubi steps
\begin {align*} \int \frac {1}{x^3-x^4-x^5+x^6} \, dx &=\int \left (\frac {1}{2 (-1+x)^2}-\frac {7}{4 (-1+x)}+\frac {1}{x^3}+\frac {1}{x^2}+\frac {2}{x}-\frac {1}{4 (1+x)}\right ) \, dx\\ &=\frac {1}{2 (1-x)}-\frac {1}{2 x^2}-\frac {1}{x}-\frac {7}{4} \log (1-x)+2 \log (x)-\frac {1}{4} \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 40, normalized size = 0.87 \[ \frac {1}{4} \left (-\frac {2}{x^2}-\frac {2}{x-1}-\frac {4}{x}-7 \log (1-x)+8 \log (x)-\log (x+1)\right ) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 41, normalized size = 0.89 \[ \frac {-3 x^2+x+1}{2 (x-1) x^2}-\frac {7}{4} \log (x-1)+2 \log (x)-\frac {1}{4} \log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 65, normalized size = 1.41 \[ -\frac {6 \, x^{2} + {\left (x^{3} - x^{2}\right )} \log \left (x + 1\right ) + 7 \, {\left (x^{3} - x^{2}\right )} \log \left (x - 1\right ) - 8 \, {\left (x^{3} - x^{2}\right )} \log \relax (x) - 2 \, x - 2}{4 \, {\left (x^{3} - x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 40, normalized size = 0.87 \[ -\frac {3 \, x^{2} - x - 1}{2 \, {\left (x - 1\right )} x^{2}} - \frac {1}{4} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {7}{4} \, \log \left ({\left | x - 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 35, normalized size = 0.76
method | result | size |
default | \(-\frac {1}{2 x^{2}}-\frac {1}{x}+2 \ln \relax (x )-\frac {1}{2 \left (-1+x \right )}-\frac {7 \ln \left (-1+x \right )}{4}-\frac {\ln \left (1+x \right )}{4}\) | \(35\) |
norman | \(\frac {\frac {1}{2}-\frac {3}{2} x^{2}+\frac {1}{2} x}{x^{2} \left (-1+x \right )}+2 \ln \relax (x )-\frac {7 \ln \left (-1+x \right )}{4}-\frac {\ln \left (1+x \right )}{4}\) | \(37\) |
risch | \(\frac {\frac {1}{2}-\frac {3}{2} x^{2}+\frac {1}{2} x}{x^{2} \left (-1+x \right )}+2 \ln \relax (x )-\frac {7 \ln \left (-1+x \right )}{4}-\frac {\ln \left (1+x \right )}{4}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 40, normalized size = 0.87 \[ -\frac {3 \, x^{2} - x - 1}{2 \, {\left (x^{3} - x^{2}\right )}} - \frac {1}{4} \, \log \left (x + 1\right ) - \frac {7}{4} \, \log \left (x - 1\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 40, normalized size = 0.87 \[ 2\,\ln \relax (x)-\frac {\ln \left (x+1\right )}{4}-\frac {7\,\ln \left (x-1\right )}{4}-\frac {-\frac {3\,x^2}{2}+\frac {x}{2}+\frac {1}{2}}{x^2-x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 37, normalized size = 0.80 \[ 2 \log {\relax (x )} - \frac {7 \log {\left (x - 1 \right )}}{4} - \frac {\log {\left (x + 1 \right )}}{4} + \frac {- 3 x^{2} + x + 1}{2 x^{3} - 2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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