Optimal. Leaf size=21 \[ \frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x) \]
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Rubi [A] time = 0.0111957, antiderivative size = 21, normalized size of antiderivative = 1., 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 1593
Rule 44
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*}
Mathematica [A] time = 0.0019447, size = 21, normalized size = 1. \[ \frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 18, normalized size = 0.9 \begin{align*}{\frac{1}{2\,{x}^{2}}}+{x}^{-1}-\ln \left ( x \right ) +\ln \left ( -1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.923482, size = 26, normalized size = 1.24 \begin{align*} \frac{2 \, x + 1}{2 \, x^{2}} + \log \left (x - 1\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86409, size = 72, normalized size = 3.43 \begin{align*} \frac{2 \, x^{2} \log \left (x - 1\right ) - 2 \, x^{2} \log \left (x\right ) + 2 \, x + 1}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097411, size = 17, normalized size = 0.81 \begin{align*} - \log{\left (x \right )} + \log{\left (x - 1 \right )} + \frac{2 x + 1}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05542, size = 28, normalized size = 1.33 \begin{align*} \frac{2 \, x + 1}{2 \, x^{2}} + \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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