Integrand size = 24, antiderivative size = 24 \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\text {Int}\left (\frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}},x\right ) \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx \\ \end{align*}
Not integrable
Time = 0.55 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92
\[\int \frac {x^{m} \arcsin \left (a x \right )^{n}}{\sqrt {-a^{2} x^{2}+1}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.50 \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\int { \frac {x^{m} \arcsin \left (a x\right )^{n}}{\sqrt {-a^{2} x^{2} + 1}} \,d x } \]
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Not integrable
Time = 4.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\int \frac {x^{m} \operatorname {asin}^{n}{\left (a x \right )}}{\sqrt {- \left (a x - 1\right ) \left (a x + 1\right )}}\, dx \]
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Exception generated. \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\text {Exception raised: RuntimeError} \]
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Timed out. \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.13 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {x^m \arcsin (a x)^n}{\sqrt {1-a^2 x^2}} \, dx=\int \frac {x^m\,{\mathrm {asin}\left (a\,x\right )}^n}{\sqrt {1-a^2\,x^2}} \,d x \]
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