Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\coth ^{-1}(a x) \sqrt{c+d x^2},x\right ) \]
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Rubi [A] time = 0.0208016, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx &=\int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx\\ \end{align*}
Mathematica [A] time = 24.1269, size = 0, normalized size = 0. \[ \int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.713, size = 0, normalized size = 0. \begin{align*} \int \sqrt{d{x}^{2}+c}{\rm arccoth} \left (ax\right )\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\sqrt{d x^{2} + c} \operatorname{arcoth}\left (a x\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{c + d x^{2}} \operatorname{acoth}{\left (a x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{d x^{2} + c} \operatorname{arcoth}\left (a x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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