Integrand size = 18, antiderivative size = 18 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {sech}(a+b x)}{x},x\right )-\text {Int}\left (\frac {\text {sech}^3(a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.05 (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 = {} \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}(a+b x)}{x} \, dx-\int \frac {\text {sech}^3(a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 15.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{3} \sinh \left (b x +a \right )^{2}}{x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 8.66 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\sinh ^{2}{\left (a + b x \right )} \operatorname {sech}^{3}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 131, normalized size of antiderivative = 7.28 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 1.77 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 2.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\text {sech}(a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {{\mathrm {sinh}\left (a+b\,x\right )}^2}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^3} \,d x \]
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