Integrand size = 25, antiderivative size = 25 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\text {Int}\left (\frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 25, 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 = {} \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx \\ \end{align*}
Not integrable
Time = 3.89 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
\[\int \frac {x^{m} \left (a +b \arcsin \left (c x \right )\right )}{-c^{2} d \,x^{2}+d}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 2.74 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=- \frac {\int \frac {a x^{m}}{c^{2} x^{2} - 1}\, dx + \int \frac {b x^{m} \operatorname {asin}{\left (c x \right )}}{c^{2} x^{2} - 1}\, dx}{d} \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 0.59 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int { -\frac {{\left (b \arcsin \left (c x\right ) + a\right )} x^{m}}{c^{2} d x^{2} - d} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {x^m (a+b \arcsin (c x))}{d-c^2 d x^2} \, dx=\int \frac {x^m\,\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}{d-c^2\,d\,x^2} \,d x \]
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