Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2},x\right ) \]
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Rubi [A] time = 0.0564397, 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 = {} \[ \int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx &=\int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx\\ \end{align*}
Mathematica [A] time = 7.0475, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.178, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{e{x}^{2}+d}\sqrt{a+b{\it Arcsinh} \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{\sqrt{a + b \operatorname{asinh}{\left (c x \right )}}}{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{\sqrt{b \operatorname{arsinh}\left (c x\right ) + a}}{e x^{2} + d}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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