Optimal. Leaf size=12 \[ -\frac {\log (2-b x)}{b} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {31}
\begin {gather*} -\frac {\log (2-b x)}{b} \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin {align*} \int \frac {1}{2-b x} \, dx &=-\frac {\log (2-b x)}{b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {\log (2-b x)}{b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 13, normalized size = 1.08
method | result | size |
norman | \(-\frac {\ln \left (b x -2\right )}{b}\) | \(12\) |
risch | \(-\frac {\ln \left (b x -2\right )}{b}\) | \(12\) |
default | \(-\frac {\ln \left (-b x +2\right )}{b}\) | \(13\) |
meijerg | \(-\frac {\ln \left (-\frac {b x}{2}+1\right )}{b}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 11, normalized size = 0.92 \begin {gather*} -\frac {\log \left (b x - 2\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.39, size = 11, normalized size = 0.92 \begin {gather*} -\frac {\log \left (b x - 2\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.67 \begin {gather*} - \frac {\log {\left (b x - 2 \right )}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.65, size = 12, normalized size = 1.00 \begin {gather*} -\frac {\log \left ({\left | b x - 2 \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 = 11, normalized size = 0.92 \begin {gather*} -\frac {\ln \left (b\,x-2\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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