Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}},x\right ) \]
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Rubi [A] time = 0.0910904, 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 = {} \[ \int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx &=\int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx\\ \end{align*}
Mathematica [A] time = 0.391118, size = 0, normalized size = 0. \[ \int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.691, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm arcsech} \left (cx\right )}{x}{\frac{1}{\sqrt{-{c}^{4}{x}^{4}+1}}}}\, 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} \, a{\left (\log \left (\sqrt{-c^{4} x^{4} + 1} + 1\right ) - \log \left (\sqrt{-c^{4} x^{4} + 1} - 1\right )\right )} + b \int \frac{\log \left (\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right )}{\sqrt{-{\left (c^{2} x^{2} + 1\right )}{\left (c x + 1\right )}{\left (c x - 1\right )}} x}\,{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{\sqrt{-c^{4} x^{4} + 1}{\left (b \operatorname{arsech}\left (c x\right ) + a\right )}}{c^{4} x^{5} - x}, 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{a + b \operatorname{asech}{\left (c x \right )}}{x \sqrt{- \left (c x - 1\right ) \left (c x + 1\right ) \left (c^{2} x^{2} + 1\right )}}\, 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{b \operatorname{arsech}\left (c x\right ) + a}{\sqrt{-c^{4} x^{4} + 1} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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