Optimal. Leaf size=24 \[ \text{Unintegrable}\left (x^m \left (a^2 c x^2+c\right )^{3/2} \tan ^{-1}(a x),x\right ) \]
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Rubi [A] time = 0.0812673, 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 = {} \[ \int x^m \left (c+a^2 c x^2\right )^{3/2} \tan ^{-1}(a x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x^m \left (c+a^2 c x^2\right )^{3/2} \tan ^{-1}(a x) \, dx &=\int x^m \left (c+a^2 c x^2\right )^{3/2} \tan ^{-1}(a x) \, dx\\ \end{align*}
Mathematica [A] time = 0.494558, size = 0, normalized size = 0. \[ \int x^m \left (c+a^2 c x^2\right )^{3/2} \tan ^{-1}(a x) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.482, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \left ({a}^{2}c{x}^{2}+c \right ) ^{{\frac{3}{2}}}\arctan \left ( ax \right ) \, 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*} \int{\left (a^{2} c x^{2} + c\right )}^{\frac{3}{2}} x^{m} \arctan \left (a x\right )\,{d x} \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^{2} c x^{2} + c\right )}^{\frac{3}{2}} x^{m} \arctan \left (a 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 [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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