Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0491233, 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 = {} \[ \int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \]
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+i a \sinh (c+d x))} \, dx &=\int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 27.5074, size = 0, normalized size = 0. \[ \int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.088, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( dx+c \right ) }{ \left ( fx+e \right ) \left ( a+ia\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{i \, \log \left (f x + e\right )}{a f} + 2 \, \int \frac{1}{-i \, a f x - i \, a e +{\left (a f x e^{c} + a 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{-i \, e^{\left (d x + c\right )} + 1}{-i \, a f x - i \, a e +{\left (a f x + a e\right )} e^{\left (d x + c\right )}}, 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 \frac{\cosh \left (d x + c\right )}{{\left (f x + e\right )}{\left (i \, a \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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