Integrand size = 18, antiderivative size = 18 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x},x\right ) \]
[Out]
Not integrable
Time = 0.16 (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 = {} \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 22.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{3} \sinh \left (b x +a \right )}{x}d x\]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 3.86 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\sinh {\left (a + b x \right )} \operatorname {sech}^{3}{\left (a + b x \right )}}{x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.30 (sec) , antiderivative size = 101, normalized size of antiderivative = 5.61 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{3} \sinh \left (b x + a\right )}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.21 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\text {sech}^2(a+b x) \tanh (a+b x)}{x} \, dx=\int \frac {\mathrm {sinh}\left (a+b\,x\right )}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^3} \,d x \]
[In]
[Out]