Integrand size = 28, antiderivative size = 28 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\text {Int}\left (\frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 28, 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 = {} \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx \\ \end{align*}
Not integrable
Time = 6.83 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx \]
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Not integrable
Time = 1.66 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93
\[\int \frac {1}{x \left (-c^{2} x^{2}+1\right )^{\frac {5}{2}} \left (a +b \arcsin \left (c x \right )\right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (-c^{2} x^{2} + 1\right )}^{\frac {5}{2}} {\left (b \arcsin \left (c x\right ) + a\right )} x} \,d x } \]
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Not integrable
Time = 4.76 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{x \left (- \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {5}{2}} \left (a + b \operatorname {asin}{\left (c x \right )}\right )}\, dx \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (-c^{2} x^{2} + 1\right )}^{\frac {5}{2}} {\left (b \arcsin \left (c x\right ) + a\right )} x} \,d x } \]
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Exception generated. \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.15 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \left (1-c^2 x^2\right )^{5/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{x\,\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,{\left (1-c^2\,x^2\right )}^{5/2}} \,d x \]
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