Optimal. Leaf size=18 \[ \frac{2 a c \log (a+b x)}{b}-c x \]
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Rubi [A] time = 0.0103672, antiderivative size = 18, 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} \[ \frac{2 a c \log (a+b x)}{b}-c x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a c-b c x}{a+b x} \, dx &=\int \left (-c+\frac{2 a c}{a+b x}\right ) \, dx\\ &=-c x+\frac{2 a c \log (a+b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0039915, size = 18, normalized size = 1. \[ c \left (\frac{2 a \log (a+b x)}{b}-x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 19, normalized size = 1.1 \begin{align*} -cx+2\,{\frac{ac\ln \left ( bx+a \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0294, size = 24, normalized size = 1.33 \begin{align*} -c x + \frac{2 \, a c \log \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41083, size = 45, normalized size = 2.5 \begin{align*} -\frac{b c x - 2 \, a c \log \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.276684, size = 15, normalized size = 0.83 \begin{align*} \frac{2 a c \log{\left (a + b x \right )}}{b} - c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04863, size = 26, normalized size = 1.44 \begin{align*} -c x + \frac{2 \, a c \log \left ({\left | b x + a \right |}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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