Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x) (a \cosh (e+f x)+a)},x\right ) \]
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Rubi [A] time = 0.0604593, 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 = {} \[ \int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx &=\int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx\\ \end{align*}
Mathematica [A] time = 8.87347, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.07, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) \left ( a+a\cosh \left ( fx+e \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*} -2 \, d \int \frac{1}{a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f +{\left (a d^{2} f x^{2} e^{e} + 2 \, a c d f x e^{e} + a c^{2} f e^{e}\right )} e^{\left (f x\right )}}\,{d x} - \frac{2}{a d f x + a c f +{\left (a d f x e^{e} + a c f e^{e}\right )} e^{\left (f x\right )}} \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{1}{a d x + a c +{\left (a d x + a c\right )} \cosh \left (f x + e\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*} \frac{\int \frac{1}{c \cosh{\left (e + f x \right )} + c + d x \cosh{\left (e + f x \right )} + d x}\, dx}{a} \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{1}{{\left (d x + c\right )}{\left (a \cosh \left (f x + e\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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