Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\sqrt{d+e x^2} \left (a+b \tan ^{-1}(c x)\right ),x\right ) \]
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Rubi [A] time = 0.0238289, 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 = {} \[ \int \sqrt{d+e x^2} \left (a+b \tan ^{-1}(c x)\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \sqrt{d+e x^2} \left (a+b \tan ^{-1}(c x)\right ) \, dx &=\int \sqrt{d+e x^2} \left (a+b \tan ^{-1}(c x)\right ) \, dx\\ \end{align*}
Mathematica [A] time = 4.702, size = 0, normalized size = 0. \[ \int \sqrt{d+e x^2} \left (a+b \tan ^{-1}(c x)\right ) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.524, size = 0, normalized size = 0. \begin{align*} \int \sqrt{e{x}^{2}+d} \left ( a+b\arctan \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 (\sqrt{e x^{2} + d}{\left (b \arctan \left (c x\right ) + a\right )}, x\right ) \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 \left (a + b \operatorname{atan}{\left (c x \right )}\right ) \sqrt{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 \sqrt{e x^{2} + d}{\left (b \arctan \left (c x\right ) + a\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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