Integrand size = 18, antiderivative size = 18 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\text {Int}\left (\frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2},x\right ) \]
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Not integrable
Time = 0.19 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 23.52 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {csch}\left (b x +a \right )^{3} \operatorname {sech}\left (b x +a \right )}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int \frac {\operatorname {csch}^{3}{\left (a + b x \right )} \operatorname {sech}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 170, normalized size of antiderivative = 9.44 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 0.50 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 2.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}(a+b x)}{x^2} \, dx=\int \frac {1}{x^2\,\mathrm {cosh}\left (a+b\,x\right )\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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