Integrand size = 10, antiderivative size = 10 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\text {Int}\left (\frac {1}{x^2 \text {arcsinh}(a x)^2},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx \\ \end{align*}
Not integrable
Time = 5.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00
\[\int \frac {1}{x^{2} \operatorname {arcsinh}\left (a x \right )^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int { \frac {1}{x^{2} \operatorname {arsinh}\left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int \frac {1}{x^{2} \operatorname {asinh}^{2}{\left (a x \right )}}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 237, normalized size of antiderivative = 23.70 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int { \frac {1}{x^{2} \operatorname {arsinh}\left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int { \frac {1}{x^{2} \operatorname {arsinh}\left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 2.67 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \text {arcsinh}(a x)^2} \, dx=\int \frac {1}{x^2\,{\mathrm {asinh}\left (a\,x\right )}^2} \,d x \]
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