Optimal. Leaf size=25 \[ \text{Unintegrable}\left (x^2 \left (d+e x^2\right )^{3/2} \left (a+b \sec ^{-1}(c x)\right ),x\right ) \]
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Rubi [A] time = 0.112009, 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 = {} \[ \int x^2 \left (d+e x^2\right )^{3/2} \left (a+b \sec ^{-1}(c x)\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x^2 \left (d+e x^2\right )^{3/2} \left (a+b \sec ^{-1}(c x)\right ) \, dx &=\int x^2 \left (d+e x^2\right )^{3/2} \left (a+b \sec ^{-1}(c x)\right ) \, dx\\ \end{align*}
Mathematica [A] time = 8.75291, size = 0, normalized size = 0. \[ \int x^2 \left (d+e x^2\right )^{3/2} \left (a+b \sec ^{-1}(c x)\right ) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.458, size = 0, normalized size = 0. \begin{align*} \int{x}^{2} \left ( e{x}^{2}+d \right ) ^{{\frac{3}{2}}} \left ( a+b{\rm arcsec} \left (cx\right ) \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 [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (a e x^{4} + a d x^{2} +{\left (b e x^{4} + b d x^{2}\right )} \operatorname{arcsec}\left (c x\right )\right )} \sqrt{e x^{2} + d}, 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{\left (e x^{2} + d\right )}^{\frac{3}{2}}{\left (b \operatorname{arcsec}\left (c x\right ) + a\right )} x^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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