Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}},x\right ) \]
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Rubi [A] time = 0.110568, 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 = {} \[ \int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx \]
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^3 \sqrt{d+e x^2}} \, dx &=\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx\\ \end{align*}
Mathematica [A] time = 22.1885, size = 0, normalized size = 0. \[ \int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.105, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm arcsech} \left (cx\right )}{{x}^{3}}{\frac{1}{\sqrt{e{x}^{2}+d}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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{e x^{2} + d}{\left (b \operatorname{arsech}\left (c x\right ) + a\right )}}{e x^{5} + d x^{3}}, 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^{3} \sqrt{d + e 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{b \operatorname{arsech}\left (c x\right ) + a}{\sqrt{e x^{2} + d} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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