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 = 15.90 (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 = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \frac {\coth \left (b x +a \right )^{3}}{x^{2}}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\coth \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.54 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {\coth ^{3}{\left (a + b x \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 175, normalized size of antiderivative = 14.58 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\coth \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int { \frac {\coth \left (b x + a\right )^{3}}{x^{2}} \,d x } \]
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Not integrable
Time = 1.82 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\coth ^3(a+b x)}{x^2} \, dx=\int \frac {{\mathrm {coth}\left (a+b\,x\right )}^3}{x^2} \,d x \]
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