Integrand size = 24, antiderivative size = 24 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\text {Int}\left (\frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx \\ \end{align*}
Not integrable
Time = 5.50 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx \]
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Not integrable
Time = 1.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83
\[\int \frac {1}{\left (-a^{2} c \,x^{2}+c \right )^{\frac {3}{2}} \sqrt {\operatorname {arccosh}\left (a x \right )}}d x\]
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Exception generated. \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 15.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {1}{\left (- c \left (a x - 1\right ) \left (a x + 1\right )\right )^{\frac {3}{2}} \sqrt {\operatorname {acosh}{\left (a x \right )}}}\, dx \]
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Not integrable
Time = 0.52 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int { \frac {1}{{\left (-a^{2} c x^{2} + c\right )}^{\frac {3}{2}} \sqrt {\operatorname {arcosh}\left (a x\right )}} \,d x } \]
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Not integrable
Time = 2.22 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int { \frac {1}{{\left (-a^{2} c x^{2} + c\right )}^{\frac {3}{2}} \sqrt {\operatorname {arcosh}\left (a x\right )}} \,d x } \]
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Not integrable
Time = 2.79 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {1}{\left (c-a^2 c x^2\right )^{3/2} \sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {1}{\sqrt {\mathrm {acosh}\left (a\,x\right )}\,{\left (c-a^2\,c\,x^2\right )}^{3/2}} \,d x \]
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