Integrand size = 18, antiderivative size = 18 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\text {Int}\left (\frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2},x\right ) \]
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Not integrable
Time = 0.17 (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 = {} \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 19.04 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {\cosh \left (b x +a \right ) \operatorname {csch}\left (b x +a \right )^{3}}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 27.85 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int \frac {\cosh {\left (a + b x \right )} \operatorname {csch}^{3}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 127, normalized size of antiderivative = 7.06 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 2.43 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\coth (a+b x) \text {csch}^2(a+b x)}{x^2} \, dx=\int \frac {\mathrm {cosh}\left (a+b\,x\right )}{x^2\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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