Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}},x\right ) \]
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Rubi [A] time = 0.0938657, 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 = {} \[ \int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx &=\int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx\\ \end{align*}
Mathematica [A] time = 13.9046, size = 0, normalized size = 0. \[ \int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 3.789, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm arccsc} \left (cx\right )}{{x}^{2}} \left ( ex+d \right ) ^{-{\frac{3}{2}}}}\, 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{\sqrt{e x + d}{\left (b \operatorname{arccsc}\left (c x\right ) + a\right )}}{e^{2} x^{4} + 2 \, d e x^{3} + d^{2} x^{2}}, 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{b \operatorname{arccsc}\left (c x\right ) + a}{{\left (e x + d\right )}^{\frac{3}{2}} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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