Optimal. Leaf size=23 \[ \text {Int}\left (\frac {x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx &=\int \frac {x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.78, size = 0, normalized size = 0.00 \[ \int \frac {x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.56, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a^{4} x^{5} - 2 \, a^{2} x^{3} + x}{\operatorname {artanh}\left (a x\right )^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (a^{2} x^{2} - 1\right )}^{2} x}{\operatorname {artanh}\left (a x\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.80, size = 0, normalized size = 0.00 \[ \int \frac {x \left (-a^{2} x^{2}+1\right )^{2}}{\arctanh \left (a x \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {2 \, {\left (a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right )}}{a \log \left (a x + 1\right ) - a \log \left (-a x + 1\right )} + \int -\frac {2 \, {\left (7 \, a^{6} x^{6} - 15 \, a^{4} x^{4} + 9 \, a^{2} x^{2} - 1\right )}}{a \log \left (a x + 1\right ) - a \log \left (-a x + 1\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x\,{\left (a^2\,x^2-1\right )}^2}{{\mathrm {atanh}\left (a\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x \left (a x - 1\right )^{2} \left (a x + 1\right )^{2}}{\operatorname {atanh}^{2}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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