Integrand size = 12, antiderivative size = 12 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\frac {(b x)^{1+m} \arcsin (a x)^3}{b (1+m)}-\frac {3 a \text {Int}\left (\frac {(b x)^{1+m} \arcsin (a x)^2}{\sqrt {1-a^2 x^2}},x\right )}{b (1+m)} \]
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Not integrable
Time = 0.07 (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 = {} \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int (b x)^m \arcsin (a x)^3 \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {(b x)^{1+m} \arcsin (a x)^3}{b (1+m)}-\frac {(3 a) \int \frac {(b x)^{1+m} \arcsin (a x)^2}{\sqrt {1-a^2 x^2}} \, dx}{b (1+m)} \\ \end{align*}
Not integrable
Time = 0.55 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int (b x)^m \arcsin (a x)^3 \, dx \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \left (b x \right )^{m} \arcsin \left (a x \right )^{3}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int { \left (b x\right )^{m} \arcsin \left (a x\right )^{3} \,d x } \]
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Not integrable
Time = 2.71 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int \left (b x\right )^{m} \operatorname {asin}^{3}{\left (a x \right )}\, dx \]
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Not integrable
Time = 0.70 (sec) , antiderivative size = 115, normalized size of antiderivative = 9.58 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int { \left (b x\right )^{m} \arcsin \left (a x\right )^{3} \,d x } \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int { \left (b x\right )^{m} \arcsin \left (a x\right )^{3} \,d x } \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^3 \, dx=\int {\mathrm {asin}\left (a\,x\right )}^3\,{\left (b\,x\right )}^m \,d x \]
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