Optimal. Leaf size=34 \[ \text{Unintegrable}\left (\frac{\sinh (c+d x) \cosh (c+d x)}{(e+f x) (a \sinh (c+d x)+b)},x\right ) \]
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Rubi [A] time = 0.107985, 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 = {} \[ \int \frac{\cosh (c+d x)}{(e+f x) (a+b \text{csch}(c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cosh (c+d x)}{(e+f x) (a+b \text{csch}(c+d x))} \, dx &=\int \frac{\cosh (c+d x) \sinh (c+d x)}{(e+f x) (b+a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 93.6895, size = 0, normalized size = 0. \[ \int \frac{\cosh (c+d x)}{(e+f x) (a+b \text{csch}(c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.303, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( dx+c \right ) }{ \left ( fx+e \right ) \left ( a+b{\rm csch} \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{e^{\left (-c + \frac{d e}{f}\right )} E_{1}\left (\frac{{\left (f x + e\right )} d}{f}\right )}{2 \, a f} - \frac{e^{\left (c - \frac{d e}{f}\right )} E_{1}\left (-\frac{{\left (f x + e\right )} d}{f}\right )}{2 \, a f} - \frac{b \log \left (f x + e\right )}{a^{2} f} + \frac{1}{2} \, \int -\frac{4 \,{\left (b^{2} e^{\left (d x + c\right )} - a b\right )}}{a^{3} f x + a^{3} e -{\left (a^{3} f x e^{\left (2 \, c\right )} + a^{3} e e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a^{2} b f x e^{c} + a^{2} b e e^{c}\right )} e^{\left (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{\cosh \left (d x + c\right )}{a f x + a e +{\left (b f x + b e\right )} \operatorname{csch}\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{\cosh{\left (c + d x \right )}}{\left (a + b \operatorname{csch}{\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{\cosh \left (d x + c\right )}{{\left (f x + e\right )}{\left (b \operatorname{csch}\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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