Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{\sin ^{-1}(a x)^n}{x^2},x\right ) \]
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Rubi [A] time = 0.0159331, 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 = {} \[ \int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx &=\int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.525123, size = 0, normalized size = 0. \[ \int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.072, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \arcsin \left ( ax \right ) \right ) ^{n}}{{x}^{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: RuntimeError} \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{\arcsin \left (a x\right )^{n}}{x^{2}}, 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{asin}^{n}{\left (a x \right )}}{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{\arcsin \left (a x\right )^{n}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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