Integrand size = 20, antiderivative size = 20 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.21 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 49.82 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {csch}\left (b x +a \right )^{2} \operatorname {sech}\left (b x +a \right )^{3}}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 0.57 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int \frac {\operatorname {csch}^{2}{\left (a + b x \right )} \operatorname {sech}^{3}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 214, normalized size of antiderivative = 10.70 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 2.06 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 2.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^3(a+b x)}{x} \, dx=\int \frac {1}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^3\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
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