Integrand size = 10, antiderivative size = 10 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\text {Int}\left (\frac {\arccos (a x)^n}{x^2},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int \frac {\arccos (a x)^n}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\arccos (a x)^n}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 0.65 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int \frac {\arccos (a x)^n}{x^2} \, dx \]
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Not integrable
Time = 0.77 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00
\[\int \frac {\arccos \left (a x \right )^{n}}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int { \frac {\arccos \left (a x\right )^{n}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int \frac {\operatorname {acos}^{n}{\left (a x \right )}}{x^{2}}\, dx \]
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Exception generated. \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\text {Exception raised: RuntimeError} \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int { \frac {\arccos \left (a x\right )^{n}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\arccos (a x)^n}{x^2} \, dx=\int \frac {{\mathrm {acos}\left (a\,x\right )}^n}{x^2} \,d x \]
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