Optimal. Leaf size=17 \[ \text{CannotIntegrate}\left (\frac{\cot ^{-1}(\coth (a+b x))}{e+f x},x\right ) \]
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Rubi [A] time = 0.0368274, 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 = {} \[ \int \frac{\cot ^{-1}(\coth (a+b x))}{e+f x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cot ^{-1}(\coth (a+b x))}{e+f x} \, dx &=\int \frac{\cot ^{-1}(\coth (a+b x))}{e+f x} \, dx\\ \end{align*}
Mathematica [A] time = 0.773464, size = 0, normalized size = 0. \[ \int \frac{\cot ^{-1}(\coth (a+b x))}{e+f x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.937, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm arccot} \left ({\rm coth} \left (bx+a\right )\right )}{fx+e}}\, 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*} \int \frac{\operatorname{arccot}\left (\coth \left (b x + a\right )\right )}{f x + e}\,{d x} \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{\operatorname{arccot}\left (\coth \left (b x + a\right )\right )}{f x + e}, 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{\operatorname{acot}{\left (\coth{\left (a + b x \right )} \right )}}{e + f 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{\operatorname{arccot}\left (\coth \left (b x + a\right )\right )}{f x + e}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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