Optimal. Leaf size=24 \[ \frac{2 x^{3/2}}{3}-\frac{x^2}{4}+4 \sqrt{x} \]
[Out]
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Rubi [A] time = 0.00846067, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{2 x^{3/2}}{3}-\frac{x^2}{4}+4 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[2/Sqrt[x] + Sqrt[x] - x/2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 x^{\frac{3}{2}}}{3} + 4 \sqrt{x} - \frac{\int x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(-1/2*x+2/x**(1/2)+x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00719066, size = 24, normalized size = 1. \[ \frac{2 x^{3/2}}{3}-\frac{x^2}{4}+4 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Integrate[2/Sqrt[x] + Sqrt[x] - x/2,x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 0.7 \[{\frac{2}{3}{x}^{{\frac{3}{2}}}}-{\frac{{x}^{2}}{4}}+4\,\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(-1/2*x+2/x^(1/2)+x^(1/2),x)
[Out]
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Maxima [A] time = 1.34178, size = 22, normalized size = 0.92 \[ -\frac{1}{4} \, x^{2} + \frac{2}{3} \, x^{\frac{3}{2}} + 4 \, \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/2*x + sqrt(x) + 2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214198, size = 19, normalized size = 0.79 \[ -\frac{1}{4} \, x^{2} + \frac{2}{3} \,{\left (x + 6\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/2*x + sqrt(x) + 2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.037598, size = 19, normalized size = 0.79 \[ \frac{2 x^{\frac{3}{2}}}{3} + 4 \sqrt{x} - \frac{x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/2*x+2/x**(1/2)+x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227877, size = 22, normalized size = 0.92 \[ -\frac{1}{4} \, x^{2} + \frac{2}{3} \, x^{\frac{3}{2}} + 4 \, \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/2*x + sqrt(x) + 2/sqrt(x),x, algorithm="giac")
[Out]