Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{a+b \coth (e+f x)}{c+d x},x\right ) \]
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Rubi [A] time = 0.0293813, 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 = {} \[ \int \frac{a+b \coth (e+f x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{a+b \coth (e+f x)}{c+d x} \, dx &=\int \frac{a+b \coth (e+f x)}{c+d x} \, dx\\ \end{align*}
Mathematica [A] time = 4.99383, size = 0, normalized size = 0. \[ \int \frac{a+b \coth (e+f x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.14, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm coth} \left (fx+e\right )}{dx+c}}\, 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*} b{\left (\frac{\log \left (d x + c\right )}{d} - \int \frac{1}{d x +{\left (d x e^{e} + c e^{e}\right )} e^{\left (f x\right )} + c}\,{d x} + \int -\frac{1}{d x -{\left (d x e^{e} + c e^{e}\right )} e^{\left (f x\right )} + c}\,{d x}\right )} + \frac{a \log \left (d x + c\right )}{d} \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 \coth \left (f x + e\right ) + a}{d x + c}, 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{a + b \coth{\left (e + f x \right )}}{c + d 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{b \coth \left (f x + e\right ) + a}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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