Optimal. Leaf size=9 \[ \sqrt{x^2+4} \]
[Out]
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Rubi [A] time = 0.00466439, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \sqrt{x^2+4} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[4 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.761721, size = 7, normalized size = 0.78 \[ \sqrt{x^{2} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**2+4)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00133305, size = 9, normalized size = 1. \[ \sqrt{x^2+4} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[4 + x^2],x]
[Out]
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Maple [A] time = 0.004, size = 8, normalized size = 0.9 \[ \sqrt{{x}^{2}+4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^2+4)^(1/2),x)
[Out]
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Maxima [A] time = 1.34601, size = 9, normalized size = 1. \[ \sqrt{x^{2} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20864, size = 41, normalized size = 4.56 \[ -\frac{x^{2} - \sqrt{x^{2} + 4} x + 4}{x - \sqrt{x^{2} + 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.152024, size = 7, normalized size = 0.78 \[ \sqrt{x^{2} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**2+4)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.200531, size = 9, normalized size = 1. \[ \sqrt{x^{2} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(x^2 + 4),x, algorithm="giac")
[Out]