Optimal. Leaf size=11 \[ \log (x)-\log (b x+1) \]
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Rubi [A] time = 0.0023277, antiderivative size = 11, 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} \[ \log (x)-\log (b x+1) \]
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 &=-\left (b \int \frac{1}{1+b x} \, dx\right )+\int \frac{1}{x} \, dx\\ &=\log (x)-\log (1+b x)\\ \end{align*}
Mathematica [A] time = 0.0055922, size = 11, normalized size = 1. \[ \log (x)-\log (b x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 12, normalized size = 1.1 \begin{align*} \ln \left ( x \right ) -\ln \left ( bx+1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0438, size = 15, normalized size = 1.36 \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 = 1.46126, size = 32, normalized size = 2.91 \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 = 0.197343, size = 8, normalized size = 0.73 \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 = 1.18662, size = 18, normalized size = 1.64 \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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