Optimal. Leaf size=14 \[ \text{Unintegrable}\left (x^m \coth ^3(a+b x),x\right ) \]
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Rubi [A] time = 0.0300256, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int x^m \coth ^3(a+b x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x^m \coth ^3(a+b x) \, dx &=\int x^m \coth ^3(a+b x) \, dx\\ \end{align*}
Mathematica [A] time = 13.9819, size = 0, normalized size = 0. \[ \int x^m \coth ^3(a+b x) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.091, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \left ( \cosh \left ( bx+a \right ) \right ) ^{3} \left ({\rm csch} \left (bx+a\right ) \right ) ^{3}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{x e^{\left (6 \, b x + m \log \left (x\right ) + 6 \, a\right )}}{{\left (m + 1\right )} e^{\left (6 \, b x + 6 \, a\right )} - 3 \,{\left (m + 1\right )} e^{\left (4 \, b x + 4 \, a\right )} + 3 \,{\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} - m - 1} + \int \frac{{\left (3 \,{\left (2 \, b x e^{\left (6 \, a\right )} +{\left (m + 1\right )} e^{\left (6 \, a\right )}\right )} e^{\left (6 \, b x\right )} - 2 \,{\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} - m - 1\right )} x^{m}}{{\left (m + 1\right )} e^{\left (8 \, b x + 8 \, a\right )} - 4 \,{\left (m + 1\right )} e^{\left (6 \, b x + 6 \, a\right )} + 6 \,{\left (m + 1\right )} e^{\left (4 \, b x + 4 \, a\right )} - 4 \,{\left (m + 1\right )} e^{\left (2 \, b x + 2 \, a\right )} + m + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (x^{m} \cosh \left (b x + a\right )^{3} \operatorname{csch}\left (b x + a\right )^{3}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \cosh \left (b x + a\right )^{3} \operatorname{csch}\left (b x + a\right )^{3}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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