Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\sqrt{d+e x^2} \left (a+b \sec ^{-1}(c x)\right )}{x^3},x\right ) \]
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Rubi [A] time = 0.101281, 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 = {} \[ \int \frac{\sqrt{d+e x^2} \left (a+b \sec ^{-1}(c x)\right )}{x^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{d+e x^2} \left (a+b \sec ^{-1}(c x)\right )}{x^3} \, dx &=\int \frac{\sqrt{d+e x^2} \left (a+b \sec ^{-1}(c x)\right )}{x^3} \, dx\\ \end{align*}
Mathematica [A] time = 4.42819, size = 0, normalized size = 0. \[ \int \frac{\sqrt{d+e x^2} \left (a+b \sec ^{-1}(c x)\right )}{x^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.26, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm arcsec} \left (cx\right )}{{x}^{3}}\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{arcsec}\left (c x\right ) + a\right )}}{x^{3}}, 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{\sqrt{e x^{2} + d}{\left (b \operatorname{arcsec}\left (c x\right ) + a\right )}}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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