Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\text {Int}\left (\frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2},x\right ) \]
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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 = {} \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx \\ \end{align*}
Not integrable
Time = 5.83 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (e x +d \right ) \left (a +b \,\operatorname {arcsinh}\left (c x \right )\right )^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.83 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 1.61 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int \frac {1}{\left (a + b \operatorname {asinh}{\left (c x \right )}\right )^{2} \left (d + e x\right )}\, dx \]
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Not integrable
Time = 0.83 (sec) , antiderivative size = 746, normalized size of antiderivative = 41.44 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int { \frac {1}{{\left (e x + d\right )} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 2.91 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d+e x) (a+b \text {arcsinh}(c x))^2} \, dx=\int \frac {1}{{\left (a+b\,\mathrm {asinh}\left (c\,x\right )\right )}^2\,\left (d+e\,x\right )} \,d x \]
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