Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{(d x)^m}{\left (a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0263933, 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 = {} \[ \int \frac{(d x)^m}{\left (a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(d x)^m}{\left (a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )\right )^2} \, dx &=\int \frac{(d x)^m}{\left (a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.389505, size = 0, normalized size = 0. \[ \int \frac{(d x)^m}{\left (a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.146, size = 0, normalized size = 0. \begin{align*} \int{ \left ( dx \right ) ^{m} \left ( a+b{\it Artanh} \left ({\frac{c}{{x}^{2}}} \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{{\left (d^{m} x^{4} - c^{2} d^{m}\right )} x^{m}}{b^{2} c x \log \left (x^{2} + c\right ) - b^{2} c x \log \left (x^{2} - c\right ) + 2 \, a b c x} + \int -\frac{{\left (d^{m}{\left (m + 3\right )} x^{4} - c^{2} d^{m}{\left (m - 1\right )}\right )} x^{m}}{b^{2} c x^{2} \log \left (x^{2} + c\right ) - b^{2} c x^{2} \log \left (x^{2} - c\right ) + 2 \, a b c x^{2}}\,{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{\left (d x\right )^{m}}{b^{2} \operatorname{artanh}\left (\frac{c}{x^{2}}\right )^{2} + 2 \, a b \operatorname{artanh}\left (\frac{c}{x^{2}}\right ) + a^{2}}, 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 \frac{\left (d x\right )^{m}}{{\left (b \operatorname{artanh}\left (\frac{c}{x^{2}}\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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