Integrand size = 12, antiderivative size = 12 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\text {Int}\left (\frac {1}{x \arcsin (a+b x)^2},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int \frac {1}{x \arcsin (a+b x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {1}{\left (-\frac {a}{b}+\frac {x}{b}\right ) \arcsin (x)^2} \, dx,x,a+b x\right )}{b} \\ \end{align*}
Not integrable
Time = 5.41 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int \frac {1}{x \arcsin (a+b x)^2} \, dx \]
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Not integrable
Time = 11.41 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \frac {1}{x \arcsin \left (b x +a \right )^{2}}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int { \frac {1}{x \arcsin \left (b x + a\right )^{2}} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int \frac {1}{x \operatorname {asin}^{2}{\left (a + b x \right )}}\, dx \]
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Not integrable
Time = 2.51 (sec) , antiderivative size = 174, normalized size of antiderivative = 14.50 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int { \frac {1}{x \arcsin \left (b x + a\right )^{2}} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int { \frac {1}{x \arcsin \left (b x + a\right )^{2}} \,d x } \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x \arcsin (a+b x)^2} \, dx=\int \frac {1}{x\,{\mathrm {asin}\left (a+b\,x\right )}^2} \,d x \]
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