Optimal. Leaf size=12 \[ -\frac {\log (1-a x)}{a} \]
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Rubi [A] time = 0.03, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {6140, 31} \[ -\frac {\log (1-a x)}{a} \]
Antiderivative was successfully verified.
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Rule 31
Rule 6140
Rubi steps
\begin {align*} \int \frac {e^{\tanh ^{-1}(a x)}}{\sqrt {1-a^2 x^2}} \, dx &=\int \frac {1}{1-a x} \, dx\\ &=-\frac {\log (1-a x)}{a}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ -\frac {\log (1-a x)}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 11, normalized size = 0.92 \[ -\frac {\log \left (a x - 1\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 12, normalized size = 1.00 \[ -\frac {\log \left ({\left | a x - 1 \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 12, normalized size = 1.00 \[ -\frac {\ln \left (a x -1\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 11, normalized size = 0.92 \[ -\frac {\log \left (a x - 1\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.92 \[ -\frac {\ln \left (a\,x-1\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 8, normalized size = 0.67 \[ - \frac {\log {\left (a x - 1 \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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