Optimal. Leaf size=27 \[ \text{Unintegrable}\left (\frac{(f x)^m \left (a+b \csc ^{-1}(c x)\right )}{\sqrt{d+e x^2}},x\right ) \]
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Rubi [A] time = 0.100059, 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 = {} \[ \int \frac{(f x)^m \left (a+b \csc ^{-1}(c x)\right )}{\sqrt{d+e x^2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(f x)^m \left (a+b \csc ^{-1}(c x)\right )}{\sqrt{d+e x^2}} \, dx &=\int \frac{(f x)^m \left (a+b \csc ^{-1}(c x)\right )}{\sqrt{d+e x^2}} \, dx\\ \end{align*}
Mathematica [A] time = 1.40697, size = 0, normalized size = 0. \[ \int \frac{(f x)^m \left (a+b \csc ^{-1}(c x)\right )}{\sqrt{d+e x^2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 7.631, size = 0, normalized size = 0. \begin{align*} \int{ \left ( fx \right ) ^{m} \left ( a+b{\rm arccsc} \left (cx\right ) \right ){\frac{1}{\sqrt{e{x}^{2}+d}}}}\, 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 \frac{{\left (b \operatorname{arccsc}\left (c x\right ) + a\right )} \left (f x\right )^{m}}{\sqrt{e x^{2} + d}}\,{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 (\frac{{\left (b \operatorname{arccsc}\left (c x\right ) + a\right )} \left (f x\right )^{m}}{\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 \frac{{\left (b \operatorname{arccsc}\left (c x\right ) + a\right )} \left (f x\right )^{m}}{\sqrt{e x^{2} + d}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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