Integrand size = 16, antiderivative size = 16 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\text {Int}\left (\frac {1}{x^2 \sqrt {a+b \arccos (c x)}},x\right ) \]
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Not integrable
Time = 0.02 (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 = {} \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx \\ \end{align*}
Not integrable
Time = 7.39 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx \]
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Not integrable
Time = 1.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88
\[\int \frac {1}{x^{2} \sqrt {a +b \arccos \left (c x \right )}}d x\]
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Exception generated. \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int \frac {1}{x^{2} \sqrt {a + b \operatorname {acos}{\left (c x \right )}}}\, dx \]
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Not integrable
Time = 0.62 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int { \frac {1}{\sqrt {b \arccos \left (c x\right ) + a} x^{2}} \,d x } \]
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Not integrable
Time = 0.65 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int { \frac {1}{\sqrt {b \arccos \left (c x\right ) + a} x^{2}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \sqrt {a+b \arccos (c x)}} \, dx=\int \frac {1}{x^2\,\sqrt {a+b\,\mathrm {acos}\left (c\,x\right )}} \,d x \]
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