Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0748446, 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 = {} \[ \int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 25.0941, size = 0, normalized size = 0. \[ \int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.111, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \cosh \left ( dx+c \right ) \right ) ^{2}}{ \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*} 2 \,{\left (a^{2} e^{c} + b^{2} e^{c}\right )} \int -\frac{e^{\left (d x\right )}}{b^{3} f x + b^{3} e -{\left (b^{3} f x e^{\left (2 \, c\right )} + b^{3} e e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a b^{2} f x e^{c} + a b^{2} e e^{c}\right )} e^{\left (d x\right )}}\,{d x} + \frac{e^{\left (-c + \frac{d e}{f}\right )} E_{1}\left (\frac{{\left (f x + e\right )} d}{f}\right )}{2 \, b f} - \frac{e^{\left (c - \frac{d e}{f}\right )} E_{1}\left (-\frac{{\left (f x + e\right )} d}{f}\right )}{2 \, b f} - \frac{a \log \left (f x + e\right )}{b^{2} f} \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 )^{2}}{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 [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 )^{2}}{{\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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