Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\text {Int}\left (\frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2},x\right ) \]
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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 = {} \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx \\ \end{align*}
Not integrable
Time = 24.11 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
\[\int \frac {1}{\sqrt {d x}\, \left (a +b \arcsin \left (c x \right )\right )^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 2.17 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{\sqrt {d x} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 4.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{\sqrt {d x} \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{2}}\, dx \]
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Not integrable
Time = 1.69 (sec) , antiderivative size = 195, normalized size of antiderivative = 10.83 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{\sqrt {d x} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{\sqrt {d x} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt {d x} (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2\,\sqrt {d\,x}} \,d x \]
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