Optimal. Leaf size=23 \[ -\frac{2 a \log (a-b x)}{b c}-\frac{x}{c} \]
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Rubi [A] time = 0.012133, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {43} \[ -\frac{2 a \log (a-b x)}{b c}-\frac{x}{c} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{a c-b c x} \, dx &=\int \left (-\frac{1}{c}+\frac{2 a}{c (a-b x)}\right ) \, dx\\ &=-\frac{x}{c}-\frac{2 a \log (a-b x)}{b c}\\ \end{align*}
Mathematica [A] time = 0.0048164, size = 23, normalized size = 1. \[ -\frac{2 a \log (a-b x)}{b c}-\frac{x}{c} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 1.1 \begin{align*} -{\frac{x}{c}}-2\,{\frac{a\ln \left ( bx-a \right ) }{bc}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02062, size = 32, normalized size = 1.39 \begin{align*} -\frac{x}{c} - \frac{2 \, a \log \left (b x - a\right )}{b c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47799, size = 45, normalized size = 1.96 \begin{align*} -\frac{b x + 2 \, a \log \left (b x - a\right )}{b c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.285939, size = 17, normalized size = 0.74 \begin{align*} - \frac{2 a \log{\left (- a + b x \right )}}{b c} - \frac{x}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05307, size = 34, normalized size = 1.48 \begin{align*} -\frac{x}{c} - \frac{2 \, a \log \left ({\left | b x - a \right |}\right )}{b c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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