Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2,x\right ) \]
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Rubi [A] time = 0.0063323, 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 = {} \[ \int \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx &=\int \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx\\ \end{align*}
Mathematica [A] time = 1.89704, size = 0, normalized size = 0. \[ \int \left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.187, size = 0, normalized size = 0. \begin{align*} \int \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}{4} \, b^{2} x \log \left (-c x^{n} + 1\right )^{2} + a^{2} x - \int -\frac{{\left (b^{2} c x^{n} - b^{2}\right )} \log \left (c x^{n} + 1\right )^{2} + 4 \,{\left (a b c x^{n} - a b\right )} \log \left (c x^{n} + 1\right ) + 2 \,{\left (2 \, a b -{\left (b^{2} c n + 2 \, a b c\right )} x^{n} -{\left (b^{2} c x^{n} - b^{2}\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} \operatorname{artanh}\left (c x^{n}\right )^{2} + 2 \, a b \operatorname{artanh}\left (c x^{n}\right ) + a^{2}, 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^{n} \right )}\right )^{2}\, 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^{n}\right ) + a\right )}^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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