Optimal. Leaf size=19 \[ \sqrt{x}+\sin \left (\sqrt{x}\right ) \cos \left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.03187, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \sqrt{x}+\sin \left (\sqrt{x}\right ) \cos \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[Cos[Sqrt[x]]^2/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 1.6876, size = 17, normalized size = 0.89 \[ \sqrt{x} + \sin{\left (\sqrt{x} \right )} \cos{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x**(1/2))**2/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0100187, size = 18, normalized size = 0.95 \[ \sqrt{x}+\frac{1}{2} \sin \left (2 \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[Sqrt[x]]^2/Sqrt[x],x]
[Out]
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Maple [A] time = 0.017, size = 14, normalized size = 0.7 \[ \cos \left ( \sqrt{x} \right ) \sin \left ( \sqrt{x} \right ) +\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x^(1/2))^2/x^(1/2),x)
[Out]
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Maxima [A] time = 1.33552, size = 16, normalized size = 0.84 \[ \sqrt{x} + \frac{1}{2} \, \sin \left (2 \, \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x))^2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226285, size = 18, normalized size = 0.95 \[ \cos \left (\sqrt{x}\right ) \sin \left (\sqrt{x}\right ) + \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x))^2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.455867, size = 39, normalized size = 2.05 \[ \sqrt{x} \sin ^{2}{\left (\sqrt{x} \right )} + \sqrt{x} \cos ^{2}{\left (\sqrt{x} \right )} + \sin{\left (\sqrt{x} \right )} \cos{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x**(1/2))**2/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.198724, size = 16, normalized size = 0.84 \[ \sqrt{x} + \frac{1}{2} \, \sin \left (2 \, \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(sqrt(x))^2/sqrt(x),x, algorithm="giac")
[Out]