Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{(a+b \coth (e+f x))^3}{(c+d x)^2},x\right ) \]
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Rubi [A] time = 0.0529811, 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 = {} \[ \int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx &=\int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 59.5268, size = 0, normalized size = 0. \[ \int \frac{(a+b \coth (e+f x))^3}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.924, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b{\rm coth} \left (fx+e\right ) \right ) ^{3}}{ \left ( dx+c \right ) ^{2}}}\, 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*} \text{result too large to display} \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{b^{3} \coth \left (f x + e\right )^{3} + 3 \, a b^{2} \coth \left (f x + e\right )^{2} + 3 \, a^{2} b \coth \left (f x + e\right ) + a^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, 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{\left (a + b \coth{\left (e + f x \right )}\right )^{3}}{\left (c + d x\right )^{2}}\, 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{{\left (b \coth \left (f x + e\right ) + a\right )}^{3}}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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