Optimal. Leaf size=31 \[ \frac {1}{4 x^2}+\frac {1}{4 x}+\frac {1}{8} \log (2-x)-\frac {\log (x)}{8} \]
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Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1593, 44} \[ \frac {1}{4 x^2}+\frac {1}{4 x}+\frac {1}{8} \log (2-x)-\frac {\log (x)}{8} \]
Antiderivative was successfully verified.
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Rule 44
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{-2 x^3+x^4} \, dx &=\int \frac {1}{(-2+x) x^3} \, dx\\ &=\int \left (\frac {1}{8 (-2+x)}-\frac {1}{2 x^3}-\frac {1}{4 x^2}-\frac {1}{8 x}\right ) \, dx\\ &=\frac {1}{4 x^2}+\frac {1}{4 x}+\frac {1}{8} \log (2-x)-\frac {\log (x)}{8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 31, normalized size = 1.00 \[ \frac {1}{4 x^2}+\frac {1}{4 x}+\frac {1}{8} \log (2-x)-\frac {\log (x)}{8} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 25, normalized size = 0.81 \[ \frac {x^{2} \log \left (x - 2\right ) - x^{2} \log \relax (x) + 2 \, x + 2}{8 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 21, normalized size = 0.68 \[ \frac {x + 1}{4 \, x^{2}} + \frac {1}{8} \, \log \left ({\left | x - 2 \right |}\right ) - \frac {1}{8} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 22, normalized size = 0.71 \[ -\frac {\ln \relax (x )}{8}+\frac {\ln \left (x -2\right )}{8}+\frac {1}{4 x}+\frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 19, normalized size = 0.61 \[ \frac {x + 1}{4 \, x^{2}} + \frac {1}{8} \, \log \left (x - 2\right ) - \frac {1}{8} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.52 \[ \frac {\frac {x}{4}+\frac {1}{4}}{x^2}-\frac {\mathrm {atanh}\left (x-1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 19, normalized size = 0.61 \[ - \frac {\log {\relax (x )}}{8} + \frac {\log {\left (x - 2 \right )}}{8} + \frac {x + 1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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