Integrand size = 30, antiderivative size = 30 \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\text {Int}\left (\frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2},x\right ) \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 30, 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 = {} \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx \\ \end{align*}
Not integrable
Time = 1.61 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx \]
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Not integrable
Time = 2.60 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
\[\int \frac {\left (f x \right )^{m} \left (-c^{2} x^{2}+1\right )^{\frac {3}{2}}}{\left (a +b \,\operatorname {arccosh}\left (c x \right )\right )^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.80 \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\int { \frac {{\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} \left (f x\right )^{m}}{{\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
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Timed out. \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\text {Timed out} \]
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Not integrable
Time = 1.95 (sec) , antiderivative size = 577, normalized size of antiderivative = 19.23 \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\int { \frac {{\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} \left (f x\right )^{m}}{{\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
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Exception generated. \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 3.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {(f x)^m \left (1-c^2 x^2\right )^{3/2}}{(a+b \text {arccosh}(c x))^2} \, dx=\int \frac {{\left (f\,x\right )}^m\,{\left (1-c^2\,x^2\right )}^{3/2}}{{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^2} \,d x \]
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