Integrand size = 12, antiderivative size = 12 \[ \int x^m \coth ^3(a+b x) \, dx=\text {Int}\left (x^m \coth ^3(a+b x),x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 12, 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 = {} \[ \int x^m \coth ^3(a+b x) \, dx=\int x^m \coth ^3(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x^m \coth ^3(a+b x) \, dx \\ \end{align*}
Not integrable
Time = 89.98 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \coth ^3(a+b x) \, dx=\int x^m \coth ^3(a+b x) \, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67
\[\int x^{m} \cosh \left (b x +a \right )^{3} \operatorname {csch}\left (b x +a \right )^{3}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int x^m \coth ^3(a+b x) \, dx=\int { x^{m} \cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3} \,d x } \]
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Timed out. \[ \int x^m \coth ^3(a+b x) \, dx=\text {Timed out} \]
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Not integrable
Time = 0.77 (sec) , antiderivative size = 173, normalized size of antiderivative = 14.42 \[ \int x^m \coth ^3(a+b x) \, dx=\int { x^{m} \cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3} \,d x } \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int x^m \coth ^3(a+b x) \, dx=\int { x^{m} \cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3} \,d x } \]
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Not integrable
Time = 2.48 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int x^m \coth ^3(a+b x) \, dx=\int \frac {x^m\,{\mathrm {cosh}\left (a+b\,x\right )}^3}{{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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