Integrand size = 12, antiderivative size = 12 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\text {Int}\left (\frac {(b x)^m}{\arcsin (a x)^2},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int \frac {(b x)^m}{\arcsin (a x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx \\ \end{align*}
Not integrable
Time = 0.32 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int \frac {(b x)^m}{\arcsin (a x)^2} \, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \frac {\left (b x \right )^{m}}{\arcsin \left (a x \right )^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.70 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int \frac {\left (b x\right )^{m}}{\operatorname {asin}^{2}{\left (a x \right )}}\, dx \]
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Not integrable
Time = 0.96 (sec) , antiderivative size = 157, normalized size of antiderivative = 13.08 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.44 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int { \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {(b x)^m}{\arcsin (a x)^2} \, dx=\int \frac {{\left (b\,x\right )}^m}{{\mathrm {asin}\left (a\,x\right )}^2} \,d x \]
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