Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{x}{(a c x+c) \tanh ^{-1}(a x)},x\right ) \]
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Rubi [A] time = 0.0405899, 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 = {} \[ \int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx &=\int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx\\ \end{align*}
Mathematica [A] time = 2.30026, size = 0, normalized size = 0. \[ \int \frac{x}{(c+a c x) \tanh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.274, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{ \left ( acx+c \right ){\it Artanh} \left ( ax \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{{\left (a c x + c\right )} \operatorname{artanh}\left (a x\right )}\,{d x} \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 (\frac{x}{{\left (a c x + c\right )} \operatorname{artanh}\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*} \frac{\int \frac{x}{a x \operatorname{atanh}{\left (a x \right )} + \operatorname{atanh}{\left (a x \right )}}\, dx}{c} \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 \frac{x}{{\left (a c x + c\right )} \operatorname{artanh}\left (a x\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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