Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}},x\right ) \]
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Rubi [A] time = 0.101614, 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 = {} \[ \int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx &=\int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx\\ \end{align*}
Mathematica [A] time = 0.93575, size = 0, normalized size = 0. \[ \int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.127, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \arcsin \left ( ax \right ) \right ) ^{n}}{{x}^{2}}{\frac{1}{\sqrt{-{a}^{2}{x}^{2}+1}}}}\, 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{\sqrt{-a^{2} x^{2} + 1} \arcsin \left (a x\right )^{n}}{a^{2} x^{4} - 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} \sqrt{- \left (a x - 1\right ) \left (a x + 1\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{\arcsin \left (a x\right )^{n}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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