Optimal. Leaf size=18 \[ \frac{\tan ^{-1}\left (\frac{3 x+2}{\sqrt{2}}\right )}{\sqrt{2}} \]
[Out]
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Rubi [A] time = 0.0269848, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{\tan ^{-1}\left (\frac{3 x+2}{\sqrt{2}}\right )}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 4*x + 3*x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.41611, size = 19, normalized size = 1.06 \[ \frac{\sqrt{2} \operatorname{atan}{\left (\sqrt{2} \left (\frac{3 x}{2} + 1\right ) \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3*x**2+4*x+2),x)
[Out]
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Mathematica [A] time = 0.00811029, size = 18, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{3 x+2}{\sqrt{2}}\right )}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 4*x + 3*x^2)^(-1),x]
[Out]
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Maple [A] time = 0.005, size = 17, normalized size = 0.9 \[{\frac{\sqrt{2}}{2}\arctan \left ({\frac{ \left ( 6\,x+4 \right ) \sqrt{2}}{4}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3*x^2+4*x+2),x)
[Out]
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Maxima [A] time = 0.794678, size = 22, normalized size = 1.22 \[ \frac{1}{2} \, \sqrt{2} \arctan \left (\frac{1}{2} \, \sqrt{2}{\left (3 \, x + 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^2 + 4*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223852, size = 22, normalized size = 1.22 \[ \frac{1}{2} \, \sqrt{2} \arctan \left (\frac{1}{2} \, \sqrt{2}{\left (3 \, x + 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^2 + 4*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.22521, size = 22, normalized size = 1.22 \[ \frac{\sqrt{2} \operatorname{atan}{\left (\frac{3 \sqrt{2} x}{2} + \sqrt{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x**2+4*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.206447, size = 22, normalized size = 1.22 \[ \frac{1}{2} \, \sqrt{2} \arctan \left (\frac{1}{2} \, \sqrt{2}{\left (3 \, x + 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^2 + 4*x + 2),x, algorithm="giac")
[Out]