Optimal. Leaf size=24 \[ \text {Int}\left (\frac {1}{\sqrt {1-a^2 x^2} \tanh ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {1}{\sqrt {1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\sqrt {1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx &=\int \frac {1}{\sqrt {1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.96, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {1-a^2 x^2} \tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.68, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-a^{2} x^{2} + 1}}{{\left (a^{2} x^{2} - 1\right )} \operatorname {artanh}\left (a x\right )^{2}}, x\right ) \]
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 \[ \int \frac {1}{\sqrt {-a^{2} x^{2} + 1} \operatorname {artanh}\left (a x\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-a^{2} x^{2}+1}\, \arctanh \left (a x \right )^{2}}\, dx \]
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 \[ \int \frac {1}{\sqrt {-a^{2} x^{2} + 1} \operatorname {artanh}\left (a x\right )^{2}}\,{d x} \]
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 \[ \int \frac {1}{{\mathrm {atanh}\left (a\,x\right )}^2\,\sqrt {1-a^2\,x^2}} \,d x \]
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 \[ \int \frac {1}{\sqrt {- \left (a x - 1\right ) \left (a x + 1\right )} \operatorname {atanh}^{2}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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