Optimal. Leaf size=21 \[ 3 x+\frac {2}{2-x}+12 \log (2-x) \]
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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 = 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*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.90 \[ 3 (x-2)-\frac {2}{x-2}+12 \log (x-2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 25, normalized size = 1.19 \[ \frac {3 \, x^{2} + 12 \, {\left (x - 2\right )} \log \left (x - 2\right ) - 6 \, x - 2}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 18, normalized size = 0.86 \[ 3 \, x - \frac {2}{x - 2} + 12 \, \log \left ({\left | x - 2 \right |}\right ) \]
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 \[ 3 x +12 \ln \left (x -2\right )-\frac {2}{x -2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 17, normalized size = 0.81 \[ 3 \, x - \frac {2}{x - 2} + 12 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 17, normalized size = 0.81 \[ 3\,x+12\,\ln \left (x-2\right )-\frac {2}{x-2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.67 \[ 3 x + 12 \log {\left (x - 2 \right )} - \frac {2}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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