Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^2\right )^2 \left (a+b \cosh ^{-1}(c x)\right )^2},x\right ) \]
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Rubi [A] time = 0.0367158, 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 = {} \[ \int \frac{1}{\left (d+e x^2\right )^2 \left (a+b \cosh ^{-1}(c x)\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (d+e x^2\right )^2 \left (a+b \cosh ^{-1}(c x)\right )^2} \, dx &=\int \frac{1}{\left (d+e x^2\right )^2 \left (a+b \cosh ^{-1}(c x)\right )^2} \, dx\\ \end{align*}
Mathematica [F] time = 180.005, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
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Maple [A] time = 0.422, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( e{x}^{2}+d \right ) ^{2} \left ( a+b{\rm arccosh} \left (cx\right ) \right ) ^{2}}}\, 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*} \text{result too large to display} \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{1}{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} +{\left (b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right )} \operatorname{arcosh}\left (c x\right )^{2} + 2 \,{\left (a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right )} \operatorname{arcosh}\left (c x\right )}, 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{1}{{\left (e x^{2} + d\right )}^{2}{\left (b \operatorname{arcosh}\left (c x\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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