Optimal. Leaf size=24 \[ \text{CannotIntegrate}\left (\frac{\tan ^{-1}(c-(-c+i) \coth (a+b x))}{x},x\right ) \]
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Rubi [A] time = 0.11197, 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 = {} \[ \int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx &=\int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx\\ \end{align*}
Mathematica [A] time = 3.62889, size = 0, normalized size = 0. \[ \int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.447, size = 0, normalized size = 0. \begin{align*} \int{\frac{\arctan \left ( c- \left ( i-c \right ){\rm coth} \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 (c\right ) + i \, \log \left (c^{2} + 1\right )\right )} \log \left (x\right ) - \frac{1}{2} \, \int \frac{\arctan \left (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 e^{\left (2 \, b x + 2 \, a\right )} - i\right )} e^{\left (-2 \, b x - 2 \, a\right )}}{c - 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{\arctan \left ({\left (c - i\right )} \coth \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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