Optimal. Leaf size=3 \[ \log \left (\coth ^{-1}(x)\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {5947} \[ \log \left (\coth ^{-1}(x)\right ) \]
Antiderivative was successfully verified.
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Rule 5947
Rubi steps
\begin {align*} \int \frac {1}{\left (1-x^2\right ) \coth ^{-1}(x)} \, dx &=\log \left (\coth ^{-1}(x)\right )\\ \end {align*}
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Mathematica [A] time = 0.03, size = 3, normalized size = 1.00 \[ \log \left (\coth ^{-1}(x)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.47, size = 11, normalized size = 3.67 \[ \log \left (\log \left (\frac {x + 1}{x - 1}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {1}{{\left (x^{2} - 1\right )} \operatorname {arcoth}\relax (x)}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 4, normalized size = 1.33 \[ \ln \left (\mathrm {arccoth}\relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 3, normalized size = 1.00 \[ \log \left (\operatorname {arcoth}\relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.30, size = 3, normalized size = 1.00 \[ \ln \left (\mathrm {acoth}\relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 3, normalized size = 1.00 \[ \log {\left (\operatorname {acoth}{\relax (x )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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