Integrand size = 10, antiderivative size = 10 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\frac {x^{1+m} \text {arccosh}(a x)^4}{1+m}-\frac {4 a \text {Int}\left (\frac {x^{1+m} \text {arccosh}(a x)^3}{\sqrt {-1+a x} \sqrt {1+a x}},x\right )}{1+m} \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 10, 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 = {} \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int x^m \text {arccosh}(a x)^4 \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {x^{1+m} \text {arccosh}(a x)^4}{1+m}-\frac {(4 a) \int \frac {x^{1+m} \text {arccosh}(a x)^3}{\sqrt {-1+a x} \sqrt {1+a x}} \, dx}{1+m} \\ \end{align*}
Not integrable
Time = 0.91 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int x^m \text {arccosh}(a x)^4 \, dx \]
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Not integrable
Time = 1.32 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00
\[\int x^{m} \operatorname {arccosh}\left (a x \right )^{4}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int { x^{m} \operatorname {arcosh}\left (a x\right )^{4} \,d x } \]
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Not integrable
Time = 27.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int x^{m} \operatorname {acosh}^{4}{\left (a x \right )}\, dx \]
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Not integrable
Time = 0.62 (sec) , antiderivative size = 152, normalized size of antiderivative = 15.20 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int { x^{m} \operatorname {arcosh}\left (a x\right )^{4} \,d x } \]
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Not integrable
Time = 0.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int { x^{m} \operatorname {arcosh}\left (a x\right )^{4} \,d x } \]
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Not integrable
Time = 2.80 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {arccosh}(a x)^4 \, dx=\int x^m\,{\mathrm {acosh}\left (a\,x\right )}^4 \,d x \]
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