Optimal. Leaf size=3 \[ \log \left (\coth ^{-1}(x)\right ) \]
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Rubi [A] time = 0.0233692, antiderivative size = 3, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0250802, size = 3, normalized size = 1. \[ \log \left (\coth ^{-1}(x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 4, normalized size = 1.3 \begin{align*} \ln \left ({\rm arccoth} \left (x\right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.975901, size = 4, normalized size = 1.33 \begin{align*} \log \left (\operatorname{arcoth}\left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.50668, size = 36, normalized size = 12. \begin{align*} \log \left (\log \left (\frac{x + 1}{x - 1}\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.411158, size = 3, normalized size = 1. \begin{align*} \log{\left (\operatorname{acoth}{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int -\frac{1}{{\left (x^{2} - 1\right )} \operatorname{arcoth}\left (x\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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