Integrand size = 20, antiderivative size = 20 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=4 \text {Int}\left (\frac {\text {csch}^2(2 a+2 b x)}{x^2},x\right ) \]
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Not integrable
Time = 0.05 (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 = {} \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 4 \int \frac {\text {csch}^2(2 a+2 b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 18.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {csch}\left (b x +a \right )^{2} \operatorname {sech}\left (b x +a \right )^{2}}{x^{2}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int \frac {\operatorname {csch}^{2}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 105, normalized size of antiderivative = 5.25 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}} \,d x } \]
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Not integrable
Time = 2.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx=\int \frac {1}{x^2\,{\mathrm {cosh}\left (a+b\,x\right )}^2\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
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