Integrand size = 16, antiderivative size = 16 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\text {Int}\left (\frac {(a+b \arccos (c x))^{5/2}}{x},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 16, 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 = {} \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.79 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx \]
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Not integrable
Time = 1.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88
\[\int \frac {\left (a +b \arccos \left (c x \right )\right )^{\frac {5}{2}}}{x}d x\]
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Exception generated. \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 38.82 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int \frac {\left (a + b \operatorname {acos}{\left (c x \right )}\right )^{\frac {5}{2}}}{x}\, dx \]
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Not integrable
Time = 0.76 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int { \frac {{\left (b \arccos \left (c x\right ) + a\right )}^{\frac {5}{2}}}{x} \,d x } \]
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Not integrable
Time = 1.11 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int { \frac {{\left (b \arccos \left (c x\right ) + a\right )}^{\frac {5}{2}}}{x} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arccos (c x))^{5/2}}{x} \, dx=\int \frac {{\left (a+b\,\mathrm {acos}\left (c\,x\right )\right )}^{5/2}}{x} \,d x \]
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