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 = {641, 31}
\begin {gather*} -\frac {\log (a-b x)}{b} \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 641
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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Maple [A]
time = 0.41, size = 13, normalized size = 1.08
method | result | size |
default | \(-\frac {\ln \left (-b x +a \right )}{b}\) | \(13\) |
norman | \(-\frac {\ln \left (-b x +a \right )}{b}\) | \(13\) |
risch | \(-\frac {\ln \left (-b x +a \right )}{b}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, 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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Fricas [A]
time = 2.52, 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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Sympy [A]
time = 0.02, 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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Giac [A]
time = 0.98, 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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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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