Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\left (a+b \tanh ^{-1}(c x)\right )^p,x\right ) \]
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Rubi [A] time = 0.0053112, 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 = {} \[ \int \left (a+b \tanh ^{-1}(c x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \left (a+b \tanh ^{-1}(c x)\right )^p \, dx &=\int \left (a+b \tanh ^{-1}(c x)\right )^p \, dx\\ \end{align*}
Mathematica [A] time = 0.441212, size = 0, normalized size = 0. \[ \int \left (a+b \tanh ^{-1}(c x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.201, size = 0, normalized size = 0. \begin{align*} \int \left ( a+b{\it Artanh} \left ( cx \right ) \right ) ^{p}\, 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{\left (b \operatorname{artanh}\left (c x\right ) + a\right )}^{p}\,{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 ({\left (b \operatorname{artanh}\left (c x\right ) + a\right )}^{p}, 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 \left (a + b \operatorname{atanh}{\left (c x \right )}\right )^{p}\, 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{\left (b \operatorname{artanh}\left (c x\right ) + a\right )}^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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