Optimal. Leaf size=21 \[ \frac {1}{2 x^2}+\frac {1}{x}+\log (1-x)-\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 21, 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} \[ \frac {1}{2 x^2}+\frac {1}{x}+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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Rule 44
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{-x^3+x^4} \, dx &=\int \frac {1}{(-1+x) x^3} \, dx\\ &=\int \left (\frac {1}{-1+x}-\frac {1}{x^3}-\frac {1}{x^2}-\frac {1}{x}\right ) \, dx\\ &=\frac {1}{2 x^2}+\frac {1}{x}+\log (1-x)-\log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ \frac {1}{2 x^2}+\frac {1}{x}+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 26, normalized size = 1.24 \[ \frac {2 \, x^{2} \log \left (x - 1\right ) - 2 \, x^{2} \log \relax (x) + 2 \, x + 1}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 21, normalized size = 1.00 \[ \frac {2 \, x + 1}{2 \, x^{2}} + \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 18, normalized size = 0.86 \[ -\ln \relax (x )+\ln \left (x -1\right )+\frac {1}{x}+\frac {1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 19, normalized size = 0.90 \[ \frac {2 \, x + 1}{2 \, x^{2}} + \log \left (x - 1\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.76 \[ \frac {x+\frac {1}{2}}{x^2}-2\,\mathrm {atanh}\left (2\,x-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 17, normalized size = 0.81 \[ - \log {\relax (x )} + \log {\left (x - 1 \right )} + \frac {2 x + 1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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