Optimal. Leaf size=33 \[ \text{Unintegrable}\left (\frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0751888, 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 = {} \[ \int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [F] time = 180.002, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
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Maple [A] time = 0.218, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \sinh \left ( dx+c \right ) \right ) ^{2}}{ \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 i \, 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{4 i \, d f x + 4 i \, d e - 4 \,{\left (d f x e^{c} + d e e^{c}\right )} e^{\left (d x\right )} - 8 i \, f}{4 \,{\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 )}} - \frac{i \, e^{\left (-c + \frac{d e}{f}\right )} E_{2}\left (\frac{{\left (f x + e\right )} d}{f}\right )}{2 \,{\left (f x + e\right )} a f} + \frac{i \, e^{\left (c - \frac{d e}{f}\right )} E_{2}\left (-\frac{{\left (f x + e\right )} d}{f}\right )}{2 \,{\left (f x + e\right )} a 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*} \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 (3 \, d x + 3 \, c\right )} +{\left (d f x + d e\right )} e^{\left (2 \, d x + 2 \, c\right )} +{\left (-i \, d f x - i \, d e - 8 i \, f\right )} e^{\left (d x + c\right )}}{2 \,{\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 (2 \, d x + 2 \, c\right )} +{\left (-2 i \, a d f^{3} x^{3} - 6 i \, a d e f^{2} x^{2} - 6 i \, a d e^{2} f x - 2 i \, a d e^{3}\right )} e^{\left (d x + c\right )}}, x\right ) - 2 i}{-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 )^{2}}{{\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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