Optimal. Leaf size=31 \[ -\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)} \]
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Rubi [A] time = 0.0218602, antiderivative size = 31, 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, 2304} \[ -\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)} \]
Antiderivative was successfully verified.
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Rule 2390
Rule 2304
Rubi steps
\begin{align*} \int \frac{\log (a+b x)}{(a+b x)^2} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{\log (x)}{x^2} \, dx,x,a+b x\right )}{b}\\ &=-\frac{1}{b (a+b x)}-\frac{\log (a+b x)}{b (a+b x)}\\ \end{align*}
Mathematica [A] time = 0.0060834, size = 21, normalized size = 0.68 \[ -\frac{\log (a+b x)+1}{a b+b^2 x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 32, normalized size = 1. \begin{align*} -{\frac{1}{b \left ( bx+a \right ) }}-{\frac{\ln \left ( bx+a \right ) }{b \left ( bx+a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.998021, size = 42, normalized size = 1.35 \begin{align*} -\frac{\log \left (b x + a\right )}{{\left (b x + a\right )} b} - \frac{1}{{\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 = 1.82127, size = 47, normalized size = 1.52 \begin{align*} -\frac{\log \left (b x + a\right ) + 1}{b^{2} x + a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.345217, size = 26, normalized size = 0.84 \begin{align*} - \frac{\log{\left (a + b x \right )}}{a b + b^{2} x} - \frac{1}{a b + b^{2} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.31106, size = 42, normalized size = 1.35 \begin{align*} -\frac{\log \left (b x + a\right )}{{\left (b x + a\right )} b} - \frac{1}{{\left (b x + a\right )} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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