Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0511999, 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 = {} \[ \int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 41.715, size = 0, normalized size = 0. \[ \int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.102, size = 0, normalized size = 0. \begin{align*} \int{\frac{\sinh \left ( dx+c \right ) }{ \left ( fx+e \right ) ^{2} \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*} -4 \, f \int \frac{1}{-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3} +{\left (a d f^{3} x^{3} e^{c} + 3 \, a d e f^{2} x^{2} e^{c} + 3 \, a d e^{2} f x e^{c} + a d e^{3} e^{c}\right )} e^{\left (d x\right )}}\,{d x} + \frac{2 \, d f x + 2 \, d e +{\left (2 i \, d f x e^{c} + 2 i \, d e e^{c}\right )} e^{\left (d x\right )} - 4 \, f}{2 \,{\left (-i \, a d f^{3} x^{2} - 2 i \, a d e f^{2} x - i \, a d e^{2} f +{\left (a d f^{3} x^{2} e^{c} + 2 \, a d e f^{2} x e^{c} + a d e^{2} f e^{c}\right )} e^{\left (d x\right )}\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*} \frac{{\left (-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} +{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (d x + c\right )}\right )}{\rm integral}\left (-\frac{d f x + d e -{\left (-i \, d f x - i \, d e\right )} e^{\left (d x + c\right )} + 4 \, f}{-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3} +{\left (a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right )} e^{\left (d x + c\right )}}, x\right ) - 2}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} +{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (d x + c\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{\sinh \left (d x + c\right )}{{\left (f x + e\right )}^{2}{\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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