Optimal. Leaf size=19 \[ -\frac{2 \tan ^{-1}\left (\frac{1-2 x}{\sqrt{3}}\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0288778, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ -\frac{2 \tan ^{-1}\left (\frac{1-2 x}{\sqrt{3}}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)/(1 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.58611, size = 22, normalized size = 1.16 \[ \frac{2 \sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{2 x}{3} - \frac{1}{3}\right ) \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)/(x**3+1),x)
[Out]
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Mathematica [A] time = 0.00913423, size = 19, normalized size = 1. \[ \frac{2 \tan ^{-1}\left (\frac{2 x-1}{\sqrt{3}}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)/(1 + x^3),x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 0.9 \[{\frac{2\,\sqrt{3}}{3}\arctan \left ({\frac{ \left ( 2\,x-1 \right ) \sqrt{3}}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)/(x^3+1),x)
[Out]
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Maxima [A] time = 1.55926, size = 22, normalized size = 1.16 \[ \frac{2}{3} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210897, size = 22, normalized size = 1.16 \[ \frac{2}{3} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.101568, size = 26, normalized size = 1.37 \[ \frac{2 \sqrt{3} \operatorname{atan}{\left (\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)/(x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.209195, size = 22, normalized size = 1.16 \[ \frac{2}{3} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + 1),x, algorithm="giac")
[Out]