Integrand size = 27, antiderivative size = 27 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\text {Int}\left (\frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2},x\right ) \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 27, 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 = {} \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx \\ \end{align*}
Not integrable
Time = 6.60 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00
\[\int \frac {x^{m} \left (a +b \arcsin \left (c x \right )\right )^{2}}{-c^{2} d \,x^{2}+d}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.59 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 3.71 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.44 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=- \frac {\int \frac {a^{2} x^{m}}{c^{2} x^{2} - 1}\, dx + \int \frac {b^{2} x^{m} \operatorname {asin}^{2}{\left (c x \right )}}{c^{2} x^{2} - 1}\, dx + \int \frac {2 a b x^{m} \operatorname {asin}{\left (c x \right )}}{c^{2} x^{2} - 1}\, dx}{d} \]
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Not integrable
Time = 0.81 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 0.93 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{d-c^2 d x^2} \, dx=\int \frac {x^m\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{d-c^2\,d\,x^2} \,d x \]
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