Integrand size = 26, antiderivative size = 26 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\text {Int}\left (\frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 26, 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 = {} \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \\ \end{align*}
Not integrable
Time = 10.62 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
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Not integrable
Time = 0.80 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00
\[\int \frac {\coth \left (d x +c \right )}{\left (f x +e \right ) \left (a +b \sinh \left (d x +c \right )\right )}d x\]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.31 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int { \frac {\coth \left (d x + c\right )}{{\left (f x + e\right )} {\left (b \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 2.56 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\coth {\left (c + d x \right )}}{\left (a + b \sinh {\left (c + d x \right )}\right ) \left (e + f x\right )}\, dx \]
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Not integrable
Time = 0.45 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int { \frac {\coth \left (d x + c\right )}{{\left (f x + e\right )} {\left (b \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.64 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int { \frac {\coth \left (d x + c\right )}{{\left (f x + e\right )} {\left (b \sinh \left (d x + c\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 1.11 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx=\int \frac {\mathrm {coth}\left (c+d\,x\right )}{\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \]
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