Integrand size = 18, antiderivative size = 18 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {csch}(a+b x)}{x},x\right )+\text {Int}\left (\frac {\text {csch}^3(a+b x)}{x},x\right ) \]
[Out]
Not integrable
Time = 0.05 (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 = {} \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {csch}(a+b x)}{x} \, dx+\int \frac {\text {csch}^3(a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 47.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
\[\int \frac {\cosh \left (b x +a \right )^{2} \operatorname {csch}\left (b x +a \right )^{3}}{x}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 51.84 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {\cosh ^{2}{\left (a + b x \right )} \operatorname {csch}^{3}{\left (a + b x \right )}}{x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.32 (sec) , antiderivative size = 157, normalized size of antiderivative = 8.72 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.71 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.36 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx=\int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
[In]
[Out]