Optimal. Leaf size=18 \[ \frac {2 a c \log (a+b x)}{b}-c x \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ c \left (\frac {2 a \log (a+b x)}{b}-x\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 20, normalized size = 1.11 \[ -\frac {b c x - 2 \, a c \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 19, normalized size = 1.06 \[ -c x + \frac {2 \, a c \log \left ({\left | b x + a \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.06 \[ \frac {2 a c \ln \left (b x +a \right )}{b}-c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 18, normalized size = 1.00 \[ -c x + \frac {2 \, a c \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 18, normalized size = 1.00 \[ \frac {2\,a\,c\,\ln \left (a+b\,x\right )}{b}-c\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.83 \[ \frac {2 a c \log {\left (a + b x \right )}}{b} - c x \]
Verification of antiderivative is not currently implemented for this CAS.
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