Optimal. Leaf size=19 \[ \frac{(a+b x) \log (a+b x)}{b}-x \]
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Rubi [A] time = 0.0058197, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2389, 2295} \[ \frac{(a+b x) \log (a+b x)}{b}-x \]
Antiderivative was successfully verified.
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Rule 2389
Rule 2295
Rubi steps
\begin{align*} \int \log (a+b x) \, dx &=\frac{\operatorname{Subst}(\int \log (x) \, dx,x,a+b x)}{b}\\ &=-x+\frac{(a+b x) \log (a+b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0044641, size = 19, normalized size = 1. \[ \frac{(a+b x) \log (a+b x)}{b}-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.056, size = 30, normalized size = 1.6 \begin{align*} \ln \left ( bx+a \right ) x+{\frac{\ln \left ( bx+a \right ) a}{b}}-x-{\frac{a}{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15998, size = 31, normalized size = 1.63 \begin{align*} -\frac{b x -{\left (b x + a\right )} \log \left (b x + a\right ) + a}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92999, size = 47, normalized size = 2.47 \begin{align*} -\frac{b x -{\left (b x + a\right )} \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 = 0.302881, size = 24, normalized size = 1.26 \begin{align*} - b \left (- \frac{a \log{\left (a + b x \right )}}{b^{2}} + \frac{x}{b}\right ) + x \log{\left (a + b x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21122, size = 31, normalized size = 1.63 \begin{align*} -\frac{b x -{\left (b x + a\right )} \log \left (b x + a\right ) + a}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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