Integrand size = 12, antiderivative size = 12 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\text {Int}\left (\frac {\coth ^2(a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int \frac {\coth ^2(a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth ^2(a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.13 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int \frac {\coth ^2(a+b x)}{x} \, dx \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67
\[\int \frac {\cosh \left (b x +a \right )^{2} \operatorname {csch}\left (b x +a \right )^{2}}{x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 21.53 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.58 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int \frac {\cosh ^{2}{\left (a + b x \right )} \operatorname {csch}^{2}{\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 69, normalized size of antiderivative = 5.75 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int { \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]
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Not integrable
Time = 2.36 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^2(a+b x)}{x} \, dx=\int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
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