Optimal. Leaf size=8 \[ \frac {1}{2} \coth ^{-1}(x)^2 \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {5949} \[ \frac {1}{2} \coth ^{-1}(x)^2 \]
Antiderivative was successfully verified.
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Rule 5949
Rubi steps
\begin {align*} \int \frac {\coth ^{-1}(x)}{1-x^2} \, dx &=\frac {1}{2} \coth ^{-1}(x)^2\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {1}{2} \coth ^{-1}(x)^2 \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 14, normalized size = 1.75 \[ \frac {1}{8} \, \log \left (\frac {x + 1}{x - 1}\right )^{2} \]
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 \[ \int -\frac {\operatorname {arcoth}\relax (x)}{x^{2} - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 1.62 \[ \arctanh \relax (x ) \mathrm {arccoth}\relax (x )-\frac {\arctanh \relax (x )^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 6, normalized size = 0.75 \[ \frac {1}{2} \, \operatorname {arcoth}\relax (x)^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.20, size = 21, normalized size = 2.62 \[ \frac {{\left (\ln \left (1-\frac {1}{x}\right )-\ln \left (\frac {1}{x}+1\right )\right )}^2}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.70, size = 5, normalized size = 0.62 \[ \frac {\operatorname {acoth}^{2}{\relax (x )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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