Integrand size = 18, antiderivative size = 18 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=b \cosh (a) \text {Chi}(b x)-\frac {\sinh (a+b x)}{x}+b \sinh (a) \text {Shi}(b x)-\text {Int}\left (\frac {\text {sech}(a+b x) \tanh (a+b x)}{x^2},x\right ) \]
[Out]
Not integrable
Time = 0.11 (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 = {} \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\sinh (a+b x)}{x^2} \, dx-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x^2} \, dx \\ & = -\frac {\sinh (a+b x)}{x}+b \int \frac {\cosh (a+b x)}{x} \, dx-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x^2} \, dx \\ & = -\frac {\sinh (a+b x)}{x}+(b \cosh (a)) \int \frac {\cosh (b x)}{x} \, dx+(b \sinh (a)) \int \frac {\sinh (b x)}{x} \, dx-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x^2} \, dx \\ & = b \cosh (a) \text {Chi}(b x)-\frac {\sinh (a+b x)}{x}+b \sinh (a) \text {Shi}(b x)-\int \frac {\text {sech}(a+b x) \tanh (a+b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 6.40 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx \]
[In]
[Out]
Not integrable
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
\[\int \frac {\operatorname {sech}\left (b x +a \right )^{2} \sinh \left (b x +a \right )^{3}}{x^{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 10.90 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int \frac {\sinh ^{3}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x^{2}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.35 (sec) , antiderivative size = 87, normalized size of antiderivative = 4.83 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int { \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\sinh (a+b x) \tanh ^2(a+b x)}{x^2} \, dx=\int \frac {{\mathrm {sinh}\left (a+b\,x\right )}^3}{x^2\,{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
[In]
[Out]