Optimal. Leaf size=22 \[ 2 \sin \left (\sqrt{x}\right )-2 \sqrt{x} \cos \left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.0173069, 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 \[ 2 \sin \left (\sqrt{x}\right )-2 \sqrt{x} \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sin[Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 2.86635, size = 46, normalized size = 2.09 \[ - \sqrt{x} e^{i \sqrt{x}} - \sqrt{x} e^{- i \sqrt{x}} - i e^{i \sqrt{x}} + i e^{- i \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00893873, size = 22, normalized size = 1. \[ 2 \sin \left (\sqrt{x}\right )-2 \sqrt{x} \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sin[Sqrt[x]],x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 0.8 \[ 2\,\sin \left ( \sqrt{x} \right ) -2\,\cos \left ( \sqrt{x} \right ) \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(x^(1/2)),x)
[Out]
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Maxima [A] time = 1.43035, size = 22, normalized size = 1. \[ -2 \, \sqrt{x} \cos \left (\sqrt{x}\right ) + 2 \, \sin \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233666, size = 22, normalized size = 1. \[ -2 \, \sqrt{x} \cos \left (\sqrt{x}\right ) + 2 \, \sin \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.389953, size = 20, normalized size = 0.91 \[ - 2 \sqrt{x} \cos{\left (\sqrt{x} \right )} + 2 \sin{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.198767, size = 22, normalized size = 1. \[ -2 \, \sqrt{x} \cos \left (\sqrt{x}\right ) + 2 \, \sin \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(sqrt(x)),x, algorithm="giac")
[Out]