Integrand size = 27, antiderivative size = 27 \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\text {Int}\left ((f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n,x\right ) \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 27, 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 = {} \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx \\ \end{align*}
Not integrable
Time = 0.40 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00
\[\int \left (f x \right )^{m} \left (-c^{2} d \,x^{2}+d \right ) \left (a +b \,\operatorname {arccosh}\left (c x \right )\right )^{n}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\int { -{\left (c^{2} d x^{2} - d\right )} \left (f x\right )^{m} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{n} \,d x } \]
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Timed out. \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\text {Timed out} \]
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Not integrable
Time = 1.05 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\int { -{\left (c^{2} d x^{2} - d\right )} \left (f x\right )^{m} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{n} \,d x } \]
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Exception generated. \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 3.15 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int (f x)^m \left (d-c^2 d x^2\right ) (a+b \text {arccosh}(c x))^n \, dx=\int {\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^n\,\left (d-c^2\,d\,x^2\right )\,{\left (f\,x\right )}^m \,d x \]
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