Integrand size = 12, antiderivative size = 12 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\text {Int}\left (\frac {\coth ^3(a+b x)}{x^2},x\right ) \]
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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 = {} \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {\coth ^3(a+b x)}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\coth ^3(a+b x)}{x^2} \, dx \\ \end{align*}
Not integrable
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {\coth ^3(a+b x)}{x^2} \, dx \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67
\[\int \frac {\cosh \left (b x +a \right )^{3} \operatorname {csch}\left (b x +a \right )^{3}}{x^{2}}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 159.59 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {\cosh ^{3}{\left (a + b x \right )} \operatorname {csch}^{3}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 175, normalized size of antiderivative = 14.58 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\cosh \left (b x + a\right )^{3} \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 2.56 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^3}{x^2\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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