Optimal. Leaf size=22 \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.0174071, 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 \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[Cos[Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 2.61152, size = 48, normalized size = 2.18 \[ - i \sqrt{x} e^{i \sqrt{x}} + i \sqrt{x} e^{- i \sqrt{x}} + e^{i \sqrt{x}} + e^{- i \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0102961, size = 22, normalized size = 1. \[ 2 \sqrt{x} \sin \left (\sqrt{x}\right )+2 \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[Sqrt[x]],x]
[Out]
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Maple [A] time = 0., size = 17, normalized size = 0.8 \[ 2\,\cos \left ( \sqrt{x} \right ) +2\,\sin \left ( \sqrt{x} \right ) \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x^(1/2)),x)
[Out]
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Maxima [A] time = 1.34485, size = 22, normalized size = 1. \[ 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23025, size = 22, normalized size = 1. \[ 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.401382, size = 20, normalized size = 0.91 \[ 2 \sqrt{x} \sin{\left (\sqrt{x} \right )} + 2 \cos{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.228569, size = 22, normalized size = 1. \[ 2 \, \sqrt{x} \sin \left (\sqrt{x}\right ) + 2 \, \cos \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x)),x, algorithm="giac")
[Out]