Integrand size = 19, antiderivative size = 46 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=\frac {1}{2 (1-x)}-\frac {1}{2 x^2}-\frac {1}{x}-\frac {7}{4} \log (1-x)+2 \log (x)-\frac {1}{4} \log (1+x) \]
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Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2083} \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=-\frac {1}{2 x^2}+\frac {1}{2 (1-x)}-\frac {1}{x}-\frac {7}{4} \log (1-x)+2 \log (x)-\frac {1}{4} \log (x+1) \]
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Rule 2083
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.02 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.87 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=\frac {1}{4} \left (-\frac {2}{-1+x}-\frac {2}{x^2}-\frac {4}{x}-7 \log (1-x)+8 \log (x)-\log (1+x)\right ) \]
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Time = 0.05 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.76
method | result | size |
default | \(-\frac {1}{2 \left (-1+x \right )}-\frac {7 \ln \left (-1+x \right )}{4}-\frac {1}{2 x^{2}}-\frac {1}{x}+2 \ln \left (x \right )-\frac {\ln \left (1+x \right )}{4}\) | \(35\) |
norman | \(\frac {\frac {1}{2}-\frac {3}{2} x^{2}+\frac {1}{2} x}{x^{2} \left (-1+x \right )}+2 \ln \left (x \right )-\frac {7 \ln \left (-1+x \right )}{4}-\frac {\ln \left (1+x \right )}{4}\) | \(37\) |
risch | \(\frac {\frac {1}{2}-\frac {3}{2} x^{2}+\frac {1}{2} x}{x^{2} \left (-1+x \right )}+2 \ln \left (x \right )-\frac {7 \ln \left (-1+x \right )}{4}-\frac {\ln \left (1+x \right )}{4}\) | \(37\) |
parallelrisch | \(\frac {8 x^{3} \ln \left (x \right )-7 \ln \left (-1+x \right ) x^{3}-\ln \left (1+x \right ) x^{3}+2-8 x^{2} \ln \left (x \right )+7 \ln \left (-1+x \right ) x^{2}+\ln \left (1+x \right ) x^{2}-6 x^{2}+2 x}{4 x^{2} \left (-1+x \right )}\) | \(70\) |
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Time = 0.24 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.41 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=-\frac {6 \, x^{2} + {\left (x^{3} - x^{2}\right )} \log \left (x + 1\right ) + 7 \, {\left (x^{3} - x^{2}\right )} \log \left (x - 1\right ) - 8 \, {\left (x^{3} - x^{2}\right )} \log \left (x\right ) - 2 \, x - 2}{4 \, {\left (x^{3} - x^{2}\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.80 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=2 \log {\left (x \right )} - \frac {7 \log {\left (x - 1 \right )}}{4} - \frac {\log {\left (x + 1 \right )}}{4} + \frac {- 3 x^{2} + x + 1}{2 x^{3} - 2 x^{2}} \]
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none
Time = 0.21 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.87 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=-\frac {3 \, x^{2} - x - 1}{2 \, {\left (x^{3} - x^{2}\right )}} - \frac {1}{4} \, \log \left (x + 1\right ) - \frac {7}{4} \, \log \left (x - 1\right ) + 2 \, \log \left (x\right ) \]
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Time = 0.29 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.87 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=-\frac {3 \, x^{2} - x - 1}{2 \, {\left (x - 1\right )} x^{2}} - \frac {1}{4} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {7}{4} \, \log \left ({\left | x - 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.25 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.87 \[ \int \frac {1}{x^3-x^4-x^5+x^6} \, dx=2\,\ln \left (x\right )-\frac {\ln \left (x+1\right )}{4}-\frac {7\,\ln \left (x-1\right )}{4}-\frac {-\frac {3\,x^2}{2}+\frac {x}{2}+\frac {1}{2}}{x^2-x^3} \]
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