Optimal. Leaf size=16 \[ \frac{1}{x}+2 \log (1-x)-2 \log (x) \]
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Rubi [A] time = 0.0062877, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {77} \[ \frac{1}{x}+2 \log (1-x)-2 \log (x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1+x}{(-1+x) x^2} \, dx &=\int \left (\frac{2}{-1+x}-\frac{1}{x^2}-\frac{2}{x}\right ) \, dx\\ &=\frac{1}{x}+2 \log (1-x)-2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.002357, size = 16, normalized size = 1. \[ \frac{1}{x}+2 \log (1-x)-2 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 15, normalized size = 0.9 \begin{align*} 2\,\ln \left ( x-1 \right ) +{x}^{-1}-2\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11391, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{x} + 2 \, \log \left (x - 1\right ) - 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20865, size = 50, normalized size = 3.12 \begin{align*} \frac{2 \, x \log \left (x - 1\right ) - 2 \, x \log \left (x\right ) + 1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09292, size = 14, normalized size = 0.88 \begin{align*} - 2 \log{\left (x \right )} + 2 \log{\left (x - 1 \right )} + \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08165, size = 22, normalized size = 1.38 \begin{align*} \frac{1}{x} + 2 \, \log \left ({\left | x - 1 \right |}\right ) - 2 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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