Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=2 \text {Int}\left (\frac {\text {csch}(2 a+2 b x)}{x},x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 2 \int \frac {\text {csch}(2 a+2 b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 13.68 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.20 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {csch}\left (b x +a \right ) \operatorname {sech}\left (b x +a \right )}{x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.54 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int \frac {\operatorname {csch}{\left (a + b x \right )} \operatorname {sech}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right ) \operatorname {sech}\left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 2.32 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int \frac {\text {csch}(a+b x) \text {sech}(a+b x)}{x} \, dx=\int \frac {1}{x\,\mathrm {cosh}\left (a+b\,x\right )\,\mathrm {sinh}\left (a+b\,x\right )} \,d x \]
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