Integrand size = 18, antiderivative size = 18 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\text {Int}\left (\frac {(d x)^{3/2}}{a+b \arccos (c x)},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx \\ \end{align*}
Not integrable
Time = 2.90 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx \]
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Not integrable
Time = 0.44 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
\[\int \frac {\left (d x \right )^{\frac {3}{2}}}{a +b \arccos \left (c x \right )}d x\]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int { \frac {\left (d x\right )^{\frac {3}{2}}}{b \arccos \left (c x\right ) + a} \,d x } \]
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Not integrable
Time = 4.13 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int \frac {\left (d x\right )^{\frac {3}{2}}}{a + b \operatorname {acos}{\left (c x \right )}}\, dx \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int { \frac {\left (d x\right )^{\frac {3}{2}}}{b \arccos \left (c x\right ) + a} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int { \frac {\left (d x\right )^{\frac {3}{2}}}{b \arccos \left (c x\right ) + a} \,d x } \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {(d x)^{3/2}}{a+b \arccos (c x)} \, dx=\int \frac {{\left (d\,x\right )}^{3/2}}{a+b\,\mathrm {acos}\left (c\,x\right )} \,d x \]
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