Optimal. Leaf size=12 \[ \log (1-b x)-\log (x) \]
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Rubi [A] time = 0.0023875, antiderivative size = 12, normalized size of antiderivative = 1., 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 36
Rule 29
Rule 31
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*}
Mathematica [A] time = 0.0028893, size = 12, normalized size = 1. \[ \log (1-b x)-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 12, normalized size = 1. \begin{align*} \ln \left ( bx-1 \right ) -\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07908, size = 15, normalized size = 1.25 \begin{align*} \log \left (b x - 1\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4917, size = 31, normalized size = 2.58 \begin{align*} \log \left (b x - 1\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131059, size = 8, normalized size = 0.67 \begin{align*} - \log{\left (x \right )} + \log{\left (x - \frac{1}{b} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13137, size = 18, normalized size = 1.5 \begin{align*} \log \left ({\left | b x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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