Optimal. Leaf size=4 \[ x+\coth (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0198524, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {3012, 8} \[ x+\coth (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3012
Rule 8
Rubi steps
\begin{align*} \int \text{csch}^2(x) \left (-1+\sinh ^2(x)\right ) \, dx &=\coth (x)+\int 1 \, dx\\ &=x+\coth (x)\\ \end{align*}
Mathematica [A] time = 0.0031859, size = 4, normalized size = 1. \[ x+\coth (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.013, size = 5, normalized size = 1.3 \begin{align*} x+{\rm coth} \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.02795, size = 16, normalized size = 4. \begin{align*} x - \frac{2}{e^{\left (-2 \, x\right )} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.99655, size = 50, normalized size = 12.5 \begin{align*} \frac{{\left (x - 1\right )} \sinh \left (x\right ) + \cosh \left (x\right )}{\sinh \left (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 [B] time = 1.11156, size = 16, normalized size = 4. \begin{align*} x + \frac{2}{e^{\left (2 \, x\right )} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]