Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}},x\right ) \]
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Rubi [A] time = 0.0567442, 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 = {} \[ \int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx &=\int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx\\ \end{align*}
Mathematica [A] time = 0.145486, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.209, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{e{x}^{2}+d}{\frac{1}{\sqrt{a+b\arcsin \left ( cx \right ) }}}}\, 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 [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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{1}{\sqrt{a + b \operatorname{asin}{\left (c x \right )}} \left (d + e x^{2}\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{1}{{\left (e x^{2} + d\right )} \sqrt{b \arcsin \left (c x\right ) + a}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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