Optimal. Leaf size=22 \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0114538, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3362, 3296, 2638} \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3362
Rule 3296
Rule 2638
Rubi steps
\begin{align*} \int \cos \left (\sqrt{x}\right ) \, dx &=2 \operatorname{Subst}\left (\int x \cos (x) \, dx,x,\sqrt{x}\right )\\ &=2 \sqrt{x} \sin \left (\sqrt{x}\right )-2 \operatorname{Subst}\left (\int \sin (x) \, dx,x,\sqrt{x}\right )\\ &=2 \cos \left (\sqrt{x}\right )+2 \sqrt{x} \sin \left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0132581, size = 22, normalized size = 1. \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 17, normalized size = 0.8 \begin{align*} 2\,\cos \left ( \sqrt{x} \right ) +2\,\sin \left ( \sqrt{x} \right ) \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.940533, size = 22, normalized size = 1. \begin{align*} 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.03848, size = 55, normalized size = 2.5 \begin{align*} 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.294535, size = 20, normalized size = 0.91 \begin{align*} 2 \sqrt{x} \sin{\left (\sqrt{x} \right )} + 2 \cos{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06754, size = 22, normalized size = 1. \begin{align*} 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]