Integrand size = 14, antiderivative size = 14 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\text {Int}\left ((b x)^{3/2} \arccos (a x)^n,x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 14, 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 = {} \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int (b x)^{3/2} \arccos (a x)^n \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (b x)^{3/2} \arccos (a x)^n \, dx \\ \end{align*}
Not integrable
Time = 1.92 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int (b x)^{3/2} \arccos (a x)^n \, dx \]
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Not integrable
Time = 0.49 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
\[\int \left (b x \right )^{\frac {3}{2}} \arccos \left (a x \right )^{n}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int { \left (b x\right )^{\frac {3}{2}} \arccos \left (a x\right )^{n} \,d x } \]
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Not integrable
Time = 162.72 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int \left (b x\right )^{\frac {3}{2}} \operatorname {acos}^{n}{\left (a x \right )}\, dx \]
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Exception generated. \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\text {Exception raised: RuntimeError} \]
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Not integrable
Time = 0.59 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int { \left (b x\right )^{\frac {3}{2}} \arccos \left (a x\right )^{n} \,d x } \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int (b x)^{3/2} \arccos (a x)^n \, dx=\int {\mathrm {acos}\left (a\,x\right )}^n\,{\left (b\,x\right )}^{3/2} \,d x \]
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