Optimal. Leaf size=18 \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
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Rubi [A] time = 0.0035481, antiderivative size = 18, 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} \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
Antiderivative was successfully verified.
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Rule 36
Rule 29
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x (a+b x)} \, dx &=\frac{\int \frac{1}{x} \, dx}{a}-\frac{b \int \frac{1}{a+b x} \, dx}{a}\\ &=\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}\\ \end{align*}
Mathematica [A] time = 0.0040577, size = 18, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 19, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( bx+a \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.95042, size = 24, normalized size = 1.33 \begin{align*} -\frac{\log \left (b x + a\right )}{a} + \frac{\log \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99473, size = 38, normalized size = 2.11 \begin{align*} -\frac{\log \left (b x + a\right ) - \log \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131829, size = 10, normalized size = 0.56 \begin{align*} \frac{\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09712, size = 27, normalized size = 1.5 \begin{align*} -\frac{\log \left ({\left | b x + a \right |}\right )}{a} + \frac{\log \left ({\left | x \right |}\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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