Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\cot ^{-1}(a x)}{\sqrt{c+d x^2}},x\right ) \]
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Rubi [A] time = 0.0221814, 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 = {} \[ \int \frac{\cot ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cot ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx &=\int \frac{\cot ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx\\ \end{align*}
Mathematica [A] time = 3.74009, size = 0, normalized size = 0. \[ \int \frac{\cot ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.858, size = 0, normalized size = 0. \begin{align*} \int{{\rm arccot} \left (ax\right ){\frac{1}{\sqrt{d{x}^{2}+c}}}}\, 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 (\frac{\operatorname{arccot}\left (a x\right )}{\sqrt{d x^{2} + c}}, 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 \frac{\operatorname{acot}{\left (a x \right )}}{\sqrt{c + d 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{\operatorname{arccot}\left (a x\right )}{\sqrt{d x^{2} + c}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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