Optimal. Leaf size=39 \[ \text{Unintegrable}\left (\frac{\coth (a+b x)}{x},x\right )+\frac{1}{2} \sinh (2 a) \text{Chi}(2 b x)+\frac{1}{2} \cosh (2 a) \text{Shi}(2 b x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.104078, 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 = {} \[ \int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x} \, dx &=\int \frac{\coth (a+b x)}{x} \, dx+\int \frac{\cosh (a+b x) \sinh (a+b x)}{x} \, dx\\ &=\int \frac{\coth (a+b x)}{x} \, dx+\int \frac{\sinh (2 a+2 b x)}{2 x} \, dx\\ &=\frac{1}{2} \int \frac{\sinh (2 a+2 b x)}{x} \, dx+\int \frac{\coth (a+b x)}{x} \, dx\\ &=\frac{1}{2} \cosh (2 a) \int \frac{\sinh (2 b x)}{x} \, dx+\frac{1}{2} \sinh (2 a) \int \frac{\cosh (2 b x)}{x} \, dx+\int \frac{\coth (a+b x)}{x} \, dx\\ &=\frac{1}{2} \text{Chi}(2 b x) \sinh (2 a)+\frac{1}{2} \cosh (2 a) \text{Shi}(2 b x)+\int \frac{\coth (a+b x)}{x} \, dx\\ \end{align*}
Mathematica [A] time = 10.9073, size = 0, normalized size = 0. \[ \int \frac{\cosh ^2(a+b x) \coth (a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.073, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \cosh \left ( bx+a \right ) \right ) ^{3}{\rm csch} \left (bx+a\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*} \frac{1}{4} \,{\rm Ei}\left (2 \, b x\right ) e^{\left (2 \, a\right )} - \frac{1}{4} \,{\rm Ei}\left (-2 \, b x\right ) e^{\left (-2 \, a\right )} - \int \frac{1}{x e^{\left (b x + a\right )} + x}\,{d x} + \int \frac{1}{x e^{\left (b x + a\right )} - x}\,{d x} + \log \left (x\right ) \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{\cosh \left (b x + a\right )^{3} \operatorname{csch}\left (b x + a\right )}{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{\cosh \left (b x + a\right )^{3} \operatorname{csch}\left (b x + a\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]