Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {sech}(a+b x) \tanh (a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.14 (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 = {} \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 6.15 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \]
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Not integrable
Time = 0.21 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{2} \sinh \left (b x +a \right )}{x}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 1.45 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\sinh {\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 60, normalized size of antiderivative = 3.75 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 2.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\mathrm {sinh}\left (a+b\,x\right )}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
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