Optimal. Leaf size=22 \[ \text{Unintegrable}\left ((c+d x)^m (a \coth (e+f x)+a)^2,x\right ) \]
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Rubi [A] time = 0.0495698, 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 = {} \[ \int (c+d x)^m (a+a \coth (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (c+d x)^m (a+a \coth (e+f x))^2 \, dx &=\int (c+d x)^m (a+a \coth (e+f x))^2 \, dx\\ \end{align*}
Mathematica [A] time = 23.6822, size = 0, normalized size = 0. \[ \int (c+d x)^m (a+a \coth (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.095, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( a+a{\rm coth} \left (fx+e\right ) \right ) ^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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 ({\left (a^{2} \coth \left (f x + e\right )^{2} + 2 \, a^{2} \coth \left (f x + e\right ) + a^{2}\right )}{\left (d x + c\right )}^{m}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} a^{2} \left (\int 2 \left (c + d x\right )^{m} \coth{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m} \coth ^{2}{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \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{\left (a \coth \left (f x + e\right ) + a\right )}^{2}{\left (d x + c\right )}^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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