Optimal. Leaf size=21 \[ \text{CannotIntegrate}\left (\frac{\tanh ^{-1}(d (-\coth (a+b x))-d+1)}{x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0888822, 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 = {} \[ \int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx &=\int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx\\ \end{align*}
Mathematica [A] time = 4.30794, size = 0, normalized size = 0. \[ \int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.322, size = 0, normalized size = 0. \begin{align*} \int -{\frac{{\it Artanh} \left ( -1+d+d{\rm coth} \left (bx+a\right ) \right ) }{x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\int \frac{\operatorname{artanh}\left (d \coth \left (b x + a\right ) + d - 1\right )}{x}\,{d x} \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{\operatorname{artanh}\left (d \coth \left (b x + a\right ) + d - 1\right )}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} - \int \frac{\operatorname{atanh}{\left (d \coth{\left (a + b x \right )} + d - 1 \right )}}{x}\, dx \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{artanh}\left (d \coth \left (b x + a\right ) + d - 1\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]