Optimal. Leaf size=15 \[ \frac{1}{4} \sqrt{4 x^2+9} \]
[Out]
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Rubi [A] time = 0.00887441, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{4} \sqrt{4 x^2+9} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[9 + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.93707, size = 10, normalized size = 0.67 \[ \frac{\sqrt{4 x^{2} + 9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(4*x**2+9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00244051, size = 15, normalized size = 1. \[ \frac{1}{4} \sqrt{4 x^2+9} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[9 + 4*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 12, normalized size = 0.8 \[{\frac{1}{4}\sqrt{4\,{x}^{2}+9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(4*x^2+9)^(1/2),x)
[Out]
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Maxima [A] time = 1.34624, size = 15, normalized size = 1. \[ \frac{1}{4} \, \sqrt{4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(4*x^2 + 9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23241, size = 51, normalized size = 3.4 \[ -\frac{4 \, x^{2} - 2 \, \sqrt{4 \, x^{2} + 9} x + 9}{4 \,{\left (2 \, x - \sqrt{4 \, x^{2} + 9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(4*x^2 + 9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.307005, size = 10, normalized size = 0.67 \[ \frac{\sqrt{4 x^{2} + 9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(4*x**2+9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216557, size = 15, normalized size = 1. \[ \frac{1}{4} \, \sqrt{4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(4*x^2 + 9),x, algorithm="giac")
[Out]