Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\coth ^3(a+b x)}{x},x\right ) \]
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Rubi [A] time = 0.0283809, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\coth ^3(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\coth ^3(a+b x)}{x} \, dx &=\int \frac{\coth ^3(a+b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 14.8989, size = 0, normalized size = 0. \[ \int \frac{\coth ^3(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.29, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm coth} \left (bx+a\right ) \right ) ^{3}}{x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{{\left (2 \, b x e^{\left (2 \, a\right )} - e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )} + 1}{b^{2} x^{2} e^{\left (4 \, b x + 4 \, a\right )} - 2 \, b^{2} x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{2}} - \int \frac{b^{2} x^{2} + 1}{b^{2} x^{3} e^{\left (b x + a\right )} + b^{2} x^{3}}\,{d x} + \int \frac{b^{2} x^{2} + 1}{b^{2} x^{3} e^{\left (b x + a\right )} - b^{2} x^{3}}\,{d x} + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\coth \left (b x + a\right )^{3}}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\coth ^{3}{\left (a + b x \right )}}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\coth \left (b x + a\right )^{3}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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