Optimal. Leaf size=38 \[ \text{Unintegrable}\left (\frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.129061, 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 = {} \[ \int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 154.862, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.777, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (dx+c\right ) \right ) ^{2} \left ({\rm sech} \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*} 16 \, b^{4} \int -\frac{e^{\left (d x + c\right )}}{8 \,{\left (a^{4} b e + a^{2} b^{3} e +{\left (a^{4} b f + a^{2} b^{3} f\right )} x -{\left (a^{4} b e e^{\left (2 \, c\right )} + a^{2} b^{3} e e^{\left (2 \, c\right )} +{\left (a^{4} b f e^{\left (2 \, c\right )} + a^{2} b^{3} f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a^{5} e e^{c} + a^{3} b^{2} e e^{c} +{\left (a^{5} f e^{c} + a^{3} b^{2} f e^{c}\right )} x\right )} e^{\left (d x\right )}\right )}}\,{d x} + \frac{2 \,{\left (a b e^{\left (3 \, d x + 3 \, c\right )} + b^{2} e^{\left (2 \, d x + 2 \, c\right )} - a b e^{\left (d x + c\right )} + 2 \, a^{2} + b^{2}\right )}}{a^{3} d e + a b^{2} d e +{\left (a^{3} d f + a b^{2} d f\right )} x -{\left (a^{3} d e e^{\left (4 \, c\right )} + a b^{2} d e e^{\left (4 \, c\right )} +{\left (a^{3} d f e^{\left (4 \, c\right )} + a b^{2} d f e^{\left (4 \, c\right )}\right )} x\right )} e^{\left (4 \, d x\right )}} - 16 \, \int -\frac{b d f x + b d e + a f}{16 \,{\left (a^{2} d f^{2} x^{2} + 2 \, a^{2} d e f x + a^{2} d e^{2} -{\left (a^{2} d f^{2} x^{2} e^{c} + 2 \, a^{2} d e f x e^{c} + a^{2} d e^{2} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} - 16 \, \int \frac{b d f x + b d e - a f}{16 \,{\left (a^{2} d f^{2} x^{2} + 2 \, a^{2} d e f x + a^{2} d e^{2} +{\left (a^{2} d f^{2} x^{2} e^{c} + 2 \, a^{2} d e f x e^{c} + a^{2} d e^{2} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} - 16 \, \int \frac{b f e^{\left (d x + c\right )} - a f}{8 \,{\left (a^{2} d e^{2} + b^{2} d e^{2} +{\left (a^{2} d f^{2} + b^{2} d f^{2}\right )} x^{2} + 2 \,{\left (a^{2} d e f + b^{2} d e f\right )} x +{\left (a^{2} d e^{2} e^{\left (2 \, c\right )} + b^{2} d e^{2} e^{\left (2 \, c\right )} +{\left (a^{2} d f^{2} e^{\left (2 \, c\right )} + b^{2} d f^{2} e^{\left (2 \, c\right )}\right )} x^{2} + 2 \,{\left (a^{2} d e f e^{\left (2 \, c\right )} + b^{2} d e f e^{\left (2 \, c\right )}\right )} x\right )} e^{\left (2 \, d x\right )}\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{\operatorname{csch}\left (d x + c\right )^{2} \operatorname{sech}\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 [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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