Integrand size = 18, antiderivative size = 18 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\text {Int}\left (\frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2},x\right ) \]
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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 = {} \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 18.93 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{3} \sinh \left (b x +a \right )}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 4.62 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int \frac {\sinh {\left (a + b x \right )} \operatorname {sech}^{3}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 100, normalized size of antiderivative = 5.56 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 2.22 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x^2} \, dx=\int \frac {\mathrm {sinh}\left (a+b\,x\right )}{x^2\,{\mathrm {cosh}\left (a+b\,x\right )}^3} \,d x \]
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