Integrand size = 22, antiderivative size = 22 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\text {Int}\left (\frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 22, 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 = {} \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx \\ \end{align*}
Not integrable
Time = 9.33 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx \]
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Not integrable
Time = 1.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int \frac {\left (a +b \arcsin \left (c x \right )\right )^{2}}{\sqrt {e \,x^{2}+d}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.55 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}{\sqrt {e x^{2} + d}} \,d x } \]
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Not integrable
Time = 3.34 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int \frac {\left (a + b \operatorname {asin}{\left (c x \right )}\right )^{2}}{\sqrt {d + e x^{2}}}\, dx \]
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Exception generated. \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\text {Exception raised: ValueError} \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}{\sqrt {e x^{2} + d}} \,d x } \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arcsin (c x))^2}{\sqrt {d+e x^2}} \, dx=\int \frac {{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{\sqrt {e\,x^2+d}} \,d x \]
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