Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\text {Int}\left (\frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx \\ \end{align*}
Not integrable
Time = 2.60 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (-a^{2} c \,x^{2}+c \right ) \arcsin \left (a x \right )}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int { -\frac {1}{{\left (a^{2} c x^{2} - c\right )} \arcsin \left (a x\right )} \,d x } \]
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Not integrable
Time = 0.75 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=- \frac {\int \frac {1}{a^{2} x^{2} \operatorname {asin}{\left (a x \right )} - \operatorname {asin}{\left (a x \right )}}\, dx}{c} \]
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Not integrable
Time = 0.38 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int { -\frac {1}{{\left (a^{2} c x^{2} - c\right )} \arcsin \left (a x\right )} \,d x } \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int { -\frac {1}{{\left (a^{2} c x^{2} - c\right )} \arcsin \left (a x\right )} \,d x } \]
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Not integrable
Time = 0.14 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (c-a^2 c x^2\right ) \arcsin (a x)} \, dx=\int \frac {1}{\mathrm {asin}\left (a\,x\right )\,\left (c-a^2\,c\,x^2\right )} \,d x \]
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