Integrand size = 18, antiderivative size = 18 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\text {Chi}(b x) \sinh (a)+\cosh (a) \text {Shi}(b x)-\text {Int}\left (\frac {\text {sech}(a+b x) \tanh (a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.10 (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 = {} \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\sinh (a+b x)}{x} \, dx-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \\ & = \cosh (a) \int \frac {\sinh (b x)}{x} \, dx+\sinh (a) \int \frac {\cosh (b x)}{x} \, dx-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \\ & = \text {Chi}(b x) \sinh (a)+\cosh (a) \text {Shi}(b x)-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 8.60 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{2} \sinh \left (b x +a \right )^{3}}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 8.51 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {\sinh ^{3}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 79, normalized size of antiderivative = 4.39 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 0.88 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x} \,d x } \]
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Not integrable
Time = 2.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x} \, dx=\int \frac {{\mathrm {sinh}\left (a+b\,x\right )}^3}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
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