Optimal. Leaf size=8 \[ 2 \sin \left (\sqrt {x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {3461, 2717}
\begin {gather*} 2 \sin \left (\sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2717
Rule 3461
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=2 \text {Subst}\left (\int \cos (x) \, dx,x,\sqrt {x}\right )\\ &=2 \sin \left (\sqrt {x}\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} 2 \sin \left (\sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 7, normalized size = 0.88
method | result | size |
derivativedivides | \(2 \sin \left (\sqrt {x}\right )\) | \(7\) |
default | \(2 \sin \left (\sqrt {x}\right )\) | \(7\) |
meijerg | \(2 \sin \left (\sqrt {x}\right )\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.41, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sin \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.60, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sin \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.11, size = 7, normalized size = 0.88 \begin {gather*} 2 \sin {\left (\sqrt {x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.45, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sin \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 6, normalized size = 0.75 \begin {gather*} 2\,\sin \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________