Optimal. Leaf size=9 \[ \frac {\log \left (\tanh ^{-1}(a x)\right )}{a} \]
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Rubi [A] time = 0.03, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {5946} \[ \frac {\log \left (\tanh ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
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Rule 5946
Rubi steps
\begin {align*} \int \frac {1}{\left (1-a^2 x^2\right ) \tanh ^{-1}(a x)} \, dx &=\frac {\log \left (\tanh ^{-1}(a x)\right )}{a}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 9, normalized size = 1.00 \[ \frac {\log \left (\tanh ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.97, size = 20, normalized size = 2.22 \[ \frac {\log \left (\log \left (-\frac {a x + 1}{a x - 1}\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 21, normalized size = 2.33 \[ \frac {\log \left ({\left | \log \left (-\frac {a x + 1}{a x - 1}\right ) \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 1.11 \[ \frac {\ln \left (\arctanh \left (a x \right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.31, size = 21, normalized size = 2.33 \[ \frac {\log \left (-\log \left (a x + 1\right ) + \log \left (-a x + 1\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.82, size = 9, normalized size = 1.00 \[ \frac {\ln \left (\mathrm {atanh}\left (a\,x\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.64, size = 7, normalized size = 0.78 \[ \frac {\log {\left (\operatorname {atanh}{\left (a x \right )} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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