Optimal. Leaf size=34 \[ \text{Unintegrable}\left (\frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0598635, 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 = {} \[ \int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [F] time = 180.001, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
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Maple [A] time = 0.421, size = 0, normalized size = 0. \begin{align*} \int{\frac{\sinh \left ( dx+c \right ) \tanh \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*} \frac{\log \left (f x + e\right )}{b f} - \frac{1}{2} \, \int -\frac{4 \,{\left (a^{3} e^{\left (d x + c\right )} - a^{2} b\right )}}{a^{2} b^{2} e + b^{4} e +{\left (a^{2} b^{2} f + b^{4} f\right )} x -{\left (a^{2} b^{2} e e^{\left (2 \, c\right )} + b^{4} e e^{\left (2 \, c\right )} +{\left (a^{2} b^{2} f e^{\left (2 \, c\right )} + b^{4} f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a^{3} b e e^{c} + a b^{3} e e^{c} +{\left (a^{3} b f e^{c} + a b^{3} f e^{c}\right )} x\right )} e^{\left (d x\right )}}\,{d x} - \frac{1}{2} \, \int \frac{4 \,{\left (a e^{\left (d x + c\right )} + b\right )}}{a^{2} e + b^{2} e +{\left (a^{2} f + b^{2} f\right )} x +{\left (a^{2} e e^{\left (2 \, c\right )} + b^{2} e e^{\left (2 \, c\right )} +{\left (a^{2} f e^{\left (2 \, c\right )} + b^{2} f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\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{\sinh \left (d x + c\right ) \tanh \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{\sinh{\left (c + d x \right )} \tanh{\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 [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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