Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\text {Int}\left (\frac {1}{(d+e x)^2 (a+b \arcsin (c x))},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx \\ \end{align*}
Not integrable
Time = 0.34 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx \]
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Not integrable
Time = 1.36 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (e x +d \right )^{2} \left (a +b \arcsin \left (c x \right )\right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.72 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (e x + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 1.78 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{\left (a + b \operatorname {asin}{\left (c x \right )}\right ) \left (d + e x\right )^{2}}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (e x + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.82 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int { \frac {1}{{\left (e x + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x)^2 (a+b \arcsin (c x))} \, dx=\int \frac {1}{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,{\left (d+e\,x\right )}^2} \,d x \]
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