Optimal. Leaf size=1 \[ x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0155451, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {4382, 8} \[ x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4382
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{\coth ^2(x)-\text{csch}^2(x)} \, dx &=\int 1 \, dx\\ &=x\\ \end{align*}
Mathematica [A] time = 0.0003987, size = 1, normalized size = 1. \[ x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] time = 0.02, size = 8, normalized size = 8. \begin{align*} 2\,{\it Artanh} \left ( \tanh \left ( x/2 \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.11078, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.97177, size = 4, normalized size = 4. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (\coth{\left (x \right )} - \operatorname{csch}{\left (x \right )}\right ) \left (\coth{\left (x \right )} + \operatorname{csch}{\left (x \right )}\right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1481, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]