Optimal. Leaf size=18 \[ x-\log (1-x)+4 \log (2-x) \]
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Rubi [A] time = 0.0079984, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214, Rules used = {703, 632, 31} \[ x-\log (1-x)+4 \log (2-x) \]
Antiderivative was successfully verified.
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Rule 703
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{x^2}{2-3 x+x^2} \, dx &=x+\int \frac{-2+3 x}{2-3 x+x^2} \, dx\\ &=x+4 \int \frac{1}{-2+x} \, dx-\int \frac{1}{-1+x} \, dx\\ &=x-\log (1-x)+4 \log (2-x)\\ \end{align*}
Mathematica [A] time = 0.0034947, size = 18, normalized size = 1. \[ x-\log (1-x)+4 \log (2-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 15, normalized size = 0.8 \begin{align*} x-\ln \left ( -1+x \right ) +4\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955964, size = 19, normalized size = 1.06 \begin{align*} x - \log \left (x - 1\right ) + 4 \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.25181, size = 42, normalized size = 2.33 \begin{align*} x - \log \left (x - 1\right ) + 4 \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.094126, size = 12, normalized size = 0.67 \begin{align*} x + 4 \log{\left (x - 2 \right )} - \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0922, size = 22, normalized size = 1.22 \begin{align*} x - \log \left ({\left | x - 1 \right |}\right ) + 4 \, \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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