Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2},x\right ) \]
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Rubi [A] time = 0.02298, 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 = {} \[ \int \frac{\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx &=\int \frac{\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 12.3515, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.109, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b{\it Artanh} \left ( c{x}^{n} \right ) \right ) ^{2}}{{x}^{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{b^{2} \log \left (-c x^{n} + 1\right )^{2}}{4 \, x} - \frac{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^{2} x^{n} - x^{2}\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{b^{2} \operatorname{artanh}\left (c x^{n}\right )^{2} + 2 \, a b \operatorname{artanh}\left (c x^{n}\right ) + a^{2}}{x^{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 \frac{\left (a + b \operatorname{atanh}{\left (c x^{n} \right )}\right )^{2}}{x^{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 \frac{{\left (b \operatorname{artanh}\left (c x^{n}\right ) + a\right )}^{2}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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