Optimal. Leaf size=18 \[ -\frac{6-x}{2 \sqrt{x^2+4}} \]
[Out]
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Rubi [A] time = 0.0181213, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{6-x}{2 \sqrt{x^2+4}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/(4 + x^2)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.76351, size = 15, normalized size = 0.83 \[ - \frac{- 2 x + 12}{4 \sqrt{x^{2} + 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(x**2+4)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0161588, size = 16, normalized size = 0.89 \[ \frac{x-6}{2 \sqrt{x^2+4}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/(4 + x^2)^(3/2),x]
[Out]
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Maple [A] time = 0.005, size = 13, normalized size = 0.7 \[{\frac{x-6}{2}{\frac{1}{\sqrt{{x}^{2}+4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(x^2+4)^(3/2),x)
[Out]
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Maxima [A] time = 0.711882, size = 27, normalized size = 1.5 \[ \frac{x}{2 \, \sqrt{x^{2} + 4}} - \frac{3}{\sqrt{x^{2} + 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(x^2 + 4)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215697, size = 43, normalized size = 2.39 \[ \frac{3 \, x - 3 \, \sqrt{x^{2} + 4} + 2}{x^{2} - \sqrt{x^{2} + 4} x + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(x^2 + 4)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.0285, size = 20, normalized size = 1.11 \[ \frac{x}{2 \sqrt{x^{2} + 4}} - \frac{3}{\sqrt{x^{2} + 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(x**2+4)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212426, size = 16, normalized size = 0.89 \[ \frac{x - 6}{2 \, \sqrt{x^{2} + 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(x^2 + 4)^(3/2),x, algorithm="giac")
[Out]