Optimal. Leaf size=17 \[ \text{CannotIntegrate}\left (\frac{\tanh ^{-1}(\cot (a+b x))}{e+f x},x\right ) \]
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Rubi [A] time = 0.0418305, 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 = {} \[ \int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx &=\int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx\\ \end{align*}
Mathematica [A] time = 0.888917, size = 0, normalized size = 0. \[ \int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.075, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it Artanh} \left ( \cot \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{artanh}\left (\cot \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{artanh}\left (\cot \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{atanh}{\left (\cot{\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{artanh}\left (\cot \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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