Optimal. Leaf size=12 \[ -\frac {\log (a-b x)}{b} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {627, 31} \begin {gather*} -\frac {\log (a-b x)}{b} \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 627
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*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {\log (a-b x)}{b} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b x}{a^2-b^2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.40, size = 13, normalized size = 1.08 \begin {gather*} -\frac {\log \left (b x - a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 14, normalized size = 1.17 \begin {gather*} -\frac {\log \left ({\left | b x - a \right |}\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 1.17 \begin {gather*} -\frac {\ln \left (b x -a \right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 13, normalized size = 1.08 \begin {gather*} -\frac {\log \left (b x - a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 1.08 \begin {gather*} -\frac {\ln \left (b\,x-a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.67 \begin {gather*} - \frac {\log {\left (- a + b x \right )}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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