Integrand size = 29, antiderivative size = 29 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\text {Int}\left (\frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 29, 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 = {} \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 1.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx \]
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Not integrable
Time = 0.66 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00
\[\int \frac {\left (f x \right )^{m} \left (a +b \,\operatorname {arccosh}\left (c x \right )\right )^{n}}{\left (-c^{2} d \,x^{2}+d \right )^{2}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int { \frac {\left (f x\right )^{m} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{n}}{{\left (c^{2} d x^{2} - d\right )}^{2}} \,d x } \]
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Timed out. \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\text {Timed out} \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int { \frac {\left (f x\right )^{m} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{n}}{{\left (c^{2} d x^{2} - d\right )}^{2}} \,d x } \]
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Not integrable
Time = 12.33 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int { \frac {\left (f x\right )^{m} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{n}}{{\left (c^{2} d x^{2} - d\right )}^{2}} \,d x } \]
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Not integrable
Time = 3.42 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^n}{\left (d-c^2 d x^2\right )^2} \, dx=\int \frac {{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^n\,{\left (f\,x\right )}^m}{{\left (d-c^2\,d\,x^2\right )}^2} \,d x \]
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