Optimal. Leaf size=16 \[ \text{Unintegrable}\left (x \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2,x\right ) \]
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Rubi [A] time = 0.0149523, 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 = {} \[ \int x \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx &=\int x \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx\\ \end{align*}
Mathematica [A] time = 8.61828, size = 0, normalized size = 0. \[ \int x \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.162, size = 0, normalized size = 0. \begin{align*} \int x \left ( a+b{\it Artanh} \left ( c{x}^{n} \right ) \right ) ^{2}\, 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*} \frac{1}{8} \, b^{2} x^{2} \log \left (-c x^{n} + 1\right )^{2} + \frac{1}{2} \, a^{2} x^{2} - \int -\frac{{\left (b^{2} c x x^{n} - b^{2} x\right )} \log \left (c x^{n} + 1\right )^{2} + 4 \,{\left (a b c x x^{n} - a b x\right )} \log \left (c x^{n} + 1\right ) +{\left (4 \, a b x -{\left (b^{2} c n + 4 \, a b c\right )} x x^{n} - 2 \,{\left (b^{2} c x x^{n} - b^{2} x\right )} \log \left (c x^{n} + 1\right )\right )} \log \left (-c x^{n} + 1\right )}{4 \,{\left (c x^{n} - 1\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 (b^{2} x \operatorname{artanh}\left (c x^{n}\right )^{2} + 2 \, a b x \operatorname{artanh}\left (c x^{n}\right ) + a^{2} x, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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^{n}\right ) + a\right )}^{2} x\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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