Optimal. Leaf size=12 \[ \log (1-b x)-\log (x) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {36, 29, 31} \[ \log (1-b x)-\log (x) \]
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rubi steps
\begin {align*} \int \frac {1}{x (-1+b x)} \, dx &=b \int \frac {1}{-1+b x} \, dx-\int \frac {1}{x} \, dx\\ &=-\log (x)+\log (1-b x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \log (1-b x)-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 11, normalized size = 0.92 \[ \log \left (b x - 1\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 13, normalized size = 1.08 \[ \log \left ({\left | b x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 1.00 \[ -\ln \relax (x )+\ln \left (b x -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 11, normalized size = 0.92 \[ \log \left (b x - 1\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 9, normalized size = 0.75 \[ -2\,\mathrm {atanh}\left (2\,b\,x-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 8, normalized size = 0.67 \[ - \log {\relax (x )} + \log {\left (x - \frac {1}{b} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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