Optimal. Leaf size=21 \[ 3 x+\frac{2}{2-x}+12 \log (2-x) \]
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Rubi [A] time = 0.0132023, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {27, 697} \[ 3 x+\frac{2}{2-x}+12 \log (2-x) \]
Antiderivative was successfully verified.
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Rule 27
Rule 697
Rubi steps
\begin{align*} \int \frac{-10+3 x^2}{4-4 x+x^2} \, dx &=\int \frac{-10+3 x^2}{(-2+x)^2} \, dx\\ &=\int \left (3+\frac{2}{(-2+x)^2}+\frac{12}{-2+x}\right ) \, dx\\ &=\frac{2}{2-x}+3 x+12 \log (2-x)\\ \end{align*}
Mathematica [A] time = 0.009009, size = 19, normalized size = 0.9 \[ 3 (x-2)-\frac{2}{x-2}+12 \log (x-2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.049, size = 18, normalized size = 0.9 \begin{align*} 3\,x-2\, \left ( -2+x \right ) ^{-1}+12\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01219, size = 23, normalized size = 1.1 \begin{align*} 3 \, x - \frac{2}{x - 2} + 12 \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67132, size = 69, normalized size = 3.29 \begin{align*} \frac{3 \, x^{2} + 12 \,{\left (x - 2\right )} \log \left (x - 2\right ) - 6 \, x - 2}{x - 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081477, size = 14, normalized size = 0.67 \begin{align*} 3 x + 12 \log{\left (x - 2 \right )} - \frac{2}{x - 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2725, size = 24, normalized size = 1.14 \begin{align*} 3 \, x - \frac{2}{x - 2} + 12 \, \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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