Optimal. Leaf size=12 \[ -\frac{\log (a-b x)}{b} \]
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Rubi [A] time = 0.0044518, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {627, 31} \[ -\frac{\log (a-b x)}{b} \]
Antiderivative was successfully verified.
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Rule 627
Rule 31
Rubi steps
\begin{align*} \int \frac{a+b x}{a^2-b^2 x^2} \, dx &=\int \frac{1}{a-b x} \, dx\\ &=-\frac{\log (a-b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0011062, size = 12, normalized size = 1. \[ -\frac{\log (a-b x)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 14, normalized size = 1.2 \begin{align*} -{\frac{\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 = 1.40966, size = 18, normalized size = 1.5 \begin{align*} -\frac{\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 = 1.73668, size = 23, normalized size = 1.92 \begin{align*} -\frac{\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 = 0.067708, size = 8, normalized size = 0.67 \begin{align*} - \frac{\log{\left (- a + b x \right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20268, size = 19, normalized size = 1.58 \begin{align*} -\frac{\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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