Integrand size = 31, antiderivative size = 31 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\text {Int}\left (\frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}},x\right ) \]
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Not integrable
Time = 0.13 (sec) , antiderivative size = 31, 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 = {} \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx \\ \end{align*}
Not integrable
Time = 4.46 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx \]
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Not integrable
Time = 3.08 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94
\[\int \frac {\left (f x \right )^{m} \left (a +b \,\operatorname {arccosh}\left (c x \right )\right )^{2}}{\left (-c^{2} d \,x^{2}+d \right )^{\frac {3}{2}}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.26 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int { \frac {{\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2} \left (f x\right )^{m}}{{\left (-c^{2} d x^{2} + d\right )}^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 26.56 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.03 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int \frac {\left (f x\right )^{m} \left (a + b \operatorname {acosh}{\left (c x \right )}\right )^{2}}{\left (- d \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {3}{2}}}\, dx \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int { \frac {{\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2} \left (f x\right )^{m}}{{\left (-c^{2} d x^{2} + d\right )}^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int { \frac {{\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2} \left (f x\right )^{m}}{{\left (-c^{2} d x^{2} + d\right )}^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 3.38 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {(f x)^m (a+b \text {arccosh}(c x))^2}{\left (d-c^2 d x^2\right )^{3/2}} \, dx=\int \frac {{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^2\,{\left (f\,x\right )}^m}{{\left (d-c^2\,d\,x^2\right )}^{3/2}} \,d x \]
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