Optimal. Leaf size=16 \[ \frac {1}{x}+2 \log (1-x)-2 \log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {1}{x}+2 \log (1-x)-2 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 18, normalized size = 1.12 \[ \frac {2 \, x \log \left (x - 1\right ) - 2 \, x \log \relax (x) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 16, normalized size = 1.00 \[ \frac {1}{x} + 2 \, \log \left ({\left | x - 1 \right |}\right ) - 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 15, normalized size = 0.94 \[ -2 \ln \relax (x )+2 \ln \left (x -1\right )+\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 14, normalized size = 0.88 \[ \frac {1}{x} + 2 \, \log \left (x - 1\right ) - 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 12, normalized size = 0.75 \[ \frac {1}{x}-4\,\mathrm {atanh}\left (2\,x-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.88 \[ - 2 \log {\relax (x )} + 2 \log {\left (x - 1 \right )} + \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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