Optimal. Leaf size=24 \[ \text{CannotIntegrate}\left (\frac{\cot ^{-1}(c-(-c+i) \tanh (a+b x))}{x},x\right ) \]
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Rubi [A] time = 0.0894306, 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 = {} \[ \int \frac{\cot ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cot ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx &=\int \frac{\cot ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx\\ \end{align*}
Mathematica [A] time = 3.21579, size = 0, normalized size = 0. \[ \int \frac{\cot ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.446, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm arccot} \left (c- \left ( i-c \right ) \tanh \left ( bx+a \right ) \right )}{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*} i \, b x + \frac{1}{4} \,{\left (2 \, \pi + 4 i \, a - 2 \, \arctan \left (1, -c\right ) + i \, \log \left (c^{2} + 1\right )\right )} \log \left (x\right ) + \frac{1}{2} \, \int \frac{\arctan \left (1, c e^{\left (2 \, b x + 2 \, a\right )}\right )}{x}\,{d x} - \frac{1}{4} i \, \int \frac{\log \left (c^{2} e^{\left (4 \, b x + 4 \, a\right )} + 1\right )}{x}\,{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{i \, \log \left (\frac{{\left (c - i\right )} e^{\left (2 \, b x + 2 \, a\right )}}{c e^{\left (2 \, b x + 2 \, a\right )} + i}\right )}{2 \, x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 ({\left (c - i\right )} \tanh \left (b x + a\right ) + c\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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