Integrand size = 16, antiderivative size = 16 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\text {Int}\left (\frac {\sqrt {a+b \arcsin (c x)}}{x^2},x\right ) \]
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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 = {} \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 5.65 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88
\[\int \frac {\sqrt {a +b \arcsin \left (c x \right )}}{x^{2}}d x\]
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Exception generated. \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int \frac {\sqrt {a + b \operatorname {asin}{\left (c x \right )}}}{x^{2}}\, dx \]
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Not integrable
Time = 0.61 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int { \frac {\sqrt {b \arcsin \left (c x\right ) + a}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.96 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int { \frac {\sqrt {b \arcsin \left (c x\right ) + a}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {a+b \arcsin (c x)}}{x^2} \, dx=\int \frac {\sqrt {a+b\,\mathrm {asin}\left (c\,x\right )}}{x^2} \,d x \]
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