Optimal. Leaf size=11 \[ -\frac {1}{2 (\sinh (x)+\cosh (x))^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {4385} \[ -\frac {1}{2 (\sinh (x)+\cosh (x))^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4385
Rubi steps
\begin {align*} \int \frac {\cosh (x)-\sinh (x)}{\cosh (x)+\sinh (x)} \, dx &=-\frac {1}{2 (\cosh (x)+\sinh (x))^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 17, normalized size = 1.55 \[ \frac {1}{2} \sinh (2 x)-\frac {1}{2} \cosh (2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.43, size = 19, normalized size = 1.73 \[ -\frac {1}{2 \, {\left (\cosh \relax (x)^{2} + 2 \, \cosh \relax (x) \sinh \relax (x) + \sinh \relax (x)^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.11, size = 6, normalized size = 0.55 \[ -\frac {1}{2} \, e^{\left (-2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 17, normalized size = 1.55 \[ -\frac {\cosh \relax (x )-\sinh \relax (x )}{2 \left (\cosh \relax (x )+\sinh \relax (x )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 6, normalized size = 0.55 \[ -\frac {1}{2} \, e^{\left (-2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.53, size = 6, normalized size = 0.55 \[ -\frac {{\mathrm {e}}^{-2\,x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.31, size = 10, normalized size = 0.91 \[ - \frac {\cosh {\relax (x )}}{\sinh {\relax (x )} + \cosh {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________