Optimal. Leaf size=2 \[ \sinh (x) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2637} \[ \sinh (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2637
Rubi steps
\begin {align*} \int \cosh (x) \, dx &=\sinh (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \sinh (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cosh (x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.20, size = 2, normalized size = 1.00 \[ \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.63, size = 11, normalized size = 5.50 \[ -\frac {1}{2} \, e^{\left (-x\right )} + \frac {1}{2} \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 3, normalized size = 1.50
method | result | size |
lookup | \(\sinh \relax (x )\) | \(3\) |
default | \(\sinh \relax (x )\) | \(3\) |
meijerg | \(\sinh \relax (x )\) | \(3\) |
risch | \(-\frac {{\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{x}}{2}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 2, normalized size = 1.00 \[ \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 2, normalized size = 1.00 \[ \mathrm {sinh}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 2, normalized size = 1.00 \[ \sinh {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________