Optimal. Leaf size=25 \[ \frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x) \]
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Rubi [A] time = 0.0105989, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {697} \[ \frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin{align*} \int \frac{1+x^2}{(-1+x)^3} \, dx &=\int \left (\frac{2}{(-1+x)^3}+\frac{2}{(-1+x)^2}+\frac{1}{-1+x}\right ) \, dx\\ &=-\frac{1}{(1-x)^2}+\frac{2}{1-x}+\log (1-x)\\ \end{align*}
Mathematica [A] time = 0.0089271, size = 16, normalized size = 0.64 \[ \frac{1-2 x}{(x-1)^2}+\log (x-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 20, normalized size = 0.8 \begin{align*} - \left ( -1+x \right ) ^{-2}+\ln \left ( -1+x \right ) -2\, \left ( -1+x \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926384, size = 30, normalized size = 1.2 \begin{align*} -\frac{2 \, x - 1}{x^{2} - 2 \, x + 1} + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.1045, size = 76, normalized size = 3.04 \begin{align*} \frac{{\left (x^{2} - 2 \, x + 1\right )} \log \left (x - 1\right ) - 2 \, x + 1}{x^{2} - 2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.088809, size = 17, normalized size = 0.68 \begin{align*} - \frac{2 x - 1}{x^{2} - 2 x + 1} + \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04723, size = 24, normalized size = 0.96 \begin{align*} -\frac{2 \, x - 1}{{\left (x - 1\right )}^{2}} + \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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