Optimal. Leaf size=15 \[ \frac{\log ^2(a+b x)}{2 b} \]
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Rubi [A] time = 0.0183944, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {2390, 2301} \[ \frac{\log ^2(a+b x)}{2 b} \]
Antiderivative was successfully verified.
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Rule 2390
Rule 2301
Rubi steps
\begin{align*} \int \frac{\log (a+b x)}{a+b x} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{b}\\ &=\frac{\log ^2(a+b x)}{2 b}\\ \end{align*}
Mathematica [A] time = 0.0016411, size = 15, normalized size = 1. \[ \frac{\log ^2(a+b x)}{2 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( bx+a \right ) \right ) ^{2}}{2\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09039, size = 18, normalized size = 1.2 \begin{align*} \frac{\log \left (b x + a\right )^{2}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78235, size = 30, normalized size = 2. \begin{align*} \frac{\log \left (b x + a\right )^{2}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.292422, size = 10, normalized size = 0.67 \begin{align*} \frac{\log{\left (a + b x \right )}^{2}}{2 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18051, size = 18, normalized size = 1.2 \begin{align*} \frac{\log \left (b x + a\right )^{2}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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