Optimal. Leaf size=22 \[ \frac{5}{1-x}-\log (1-x)+3 \log (x) \]
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Rubi [A] time = 0.0133821, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {894} \[ \frac{5}{1-x}-\log (1-x)+3 \log (x) \]
Antiderivative was successfully verified.
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Rule 894
Rubi steps
\begin{align*} \int \frac{3+2 x^2}{(-1+x)^2 x} \, dx &=\int \left (\frac{1}{1-x}+\frac{5}{(-1+x)^2}+\frac{3}{x}\right ) \, dx\\ &=\frac{5}{1-x}-\log (1-x)+3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0095116, size = 20, normalized size = 0.91 \[ -\frac{5}{x-1}-\log (1-x)+3 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 19, normalized size = 0.9 \begin{align*} -5\, \left ( x-1 \right ) ^{-1}-\ln \left ( x-1 \right ) +3\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986294, size = 24, normalized size = 1.09 \begin{align*} -\frac{5}{x - 1} - \log \left (x - 1\right ) + 3 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2272, size = 73, normalized size = 3.32 \begin{align*} -\frac{{\left (x - 1\right )} \log \left (x - 1\right ) - 3 \,{\left (x - 1\right )} \log \left (x\right ) + 5}{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.102487, size = 14, normalized size = 0.64 \begin{align*} 3 \log{\left (x \right )} - \log{\left (x - 1 \right )} - \frac{5}{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17183, size = 38, normalized size = 1.73 \begin{align*} -\frac{5}{x - 1} + 2 \, \log \left ({\left | x - 1 \right |}\right ) + 3 \, \log \left ({\left | -\frac{1}{x - 1} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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