Integrand size = 32, antiderivative size = 32 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\text {Int}\left (\frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \\ \end{align*}
Not integrable
Time = 76.91 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
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Not integrable
Time = 0.69 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00
\[\int \frac {\coth \left (d x +c \right ) \operatorname {csch}\left (d x +c \right )}{\left (f x +e \right ) \left (a +b \sinh \left (d x +c \right )\right )}d x\]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.25 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int { \frac {\coth \left (d x + c\right ) \operatorname {csch}\left (d x + c\right )}{{\left (f x + e\right )} {\left (b \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 5.56 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.91 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth {\left (c + d x \right )} \operatorname {csch}{\left (c + d x \right )}}{\left (a + b \sinh {\left (c + d x \right )}\right ) \left (e + f x\right )}\, dx \]
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Not integrable
Time = 0.52 (sec) , antiderivative size = 316, normalized size of antiderivative = 9.88 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int { \frac {\coth \left (d x + c\right ) \operatorname {csch}\left (d x + c\right )}{{\left (f x + e\right )} {\left (b \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Timed out. \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\text {Timed out} \]
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Not integrable
Time = 1.82 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {\coth (c+d x) \text {csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\mathrm {coth}\left (c+d\,x\right )}{\mathrm {sinh}\left (c+d\,x\right )\,\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \]
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