Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sin ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0133543, 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 = {} \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx &=\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 6.43086, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2} \left ( \arcsin \left ( ax \right ) \right ) ^{3}}}\, 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*} -\frac{x^{3} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{2} \int \frac{a^{2} x^{2} - 6}{x^{4} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}\,{d x} + \sqrt{a x + 1} \sqrt{-a x + 1} a x +{\left (a^{2} x^{2} - 2\right )} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}{2 \, a^{2} x^{3} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{2}} \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{1}{x^{2} \arcsin \left (a x\right )^{3}}, 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{1}{x^{2} \operatorname{asin}^{3}{\left (a x \right )}}\, 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{1}{x^{2} \arcsin \left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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