Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.049565, 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 = {} \[ \int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 29.0795, size = 0, normalized size = 0. \[ \int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.379, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm coth} \left (dx+c\right )}{ \left ( fx+e \right ) \left ( a+b\sinh \left ( dx+c \right ) \right ) }}\, 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*} \int \frac{\coth \left (d x + c\right )}{{\left (f x + e\right )}{\left (b \sinh \left (d x + c\right ) + a\right )}}\,{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 (\frac{\coth \left (d x + c\right )}{a f x + a e +{\left (b f x + b e\right )} \sinh \left (d x + c\right )}, 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*} \int \frac{\coth{\left (c + d x \right )}}{\left (a + b \sinh{\left (c + d x \right )}\right ) \left (e + f x\right )}\, dx \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 \frac{\coth \left (d x + c\right )}{{\left (f x + e\right )}{\left (b \sinh \left (d x + c\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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