Optimal. Leaf size=24 \[ \text{CannotIntegrate}\left (\frac{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.163922, 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 = {} \[ \int \frac{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx &=\int \frac{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx\\ \end{align*}
Mathematica [A] time = 0.770654, size = 0, normalized size = 0. \[ \int \frac{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.407, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm arccot} \left (c- \left ( 1-ic \right ) \tan \left ( bx+a \right ) \right )}{x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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 i \, b x + 2 i \, a\right )}}{c e^{\left (2 i \, b x + 2 i \, a\right )} - i}\right )}{2 \, x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arccot}\left (-{\left (-i \, c + 1\right )} \tan \left (b x + a\right ) + c\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]