Integrand size = 16, antiderivative size = 16 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\text {Int}\left (\frac {\coth (a+b x) \text {csch}(a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 16, 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 = {} \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 22.78 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12
\[\int \frac {\cosh \left (b x +a \right ) \operatorname {csch}\left (b x +a \right )^{2}}{x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 9.12 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\cosh {\left (a + b x \right )} \operatorname {csch}^{2}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 79, normalized size of antiderivative = 4.94 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 0.47 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 2.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\coth (a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\mathrm {cosh}\left (a+b\,x\right )}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
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