Optimal. Leaf size=14 \[ \frac{1}{6} \tan ^{-1}\left (\frac{1}{3} \left (x^2+1\right )\right ) \]
[Out]
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Rubi [A] time = 0.0351037, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{1}{6} \tan ^{-1}\left (\frac{1}{3} \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
[In] Int[x/(10 + 2*x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 4.7103, size = 10, normalized size = 0.71 \[ \frac{\operatorname{atan}{\left (\frac{x^{2}}{3} + \frac{1}{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**4+2*x**2+10),x)
[Out]
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Mathematica [A] time = 0.00851059, size = 14, normalized size = 1. \[ \frac{1}{6} \tan ^{-1}\left (\frac{1}{3} \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/(10 + 2*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.004, size = 11, normalized size = 0.8 \[{\frac{1}{6}\arctan \left ({\frac{{x}^{2}}{3}}+{\frac{1}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^4+2*x^2+10),x)
[Out]
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Maxima [A] time = 0.761683, size = 14, normalized size = 1. \[ \frac{1}{6} \, \arctan \left (\frac{1}{3} \, x^{2} + \frac{1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 10),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269194, size = 14, normalized size = 1. \[ \frac{1}{6} \, \arctan \left (\frac{1}{3} \, x^{2} + \frac{1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 10),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.187189, size = 10, normalized size = 0.71 \[ \frac{\operatorname{atan}{\left (\frac{x^{2}}{3} + \frac{1}{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**4+2*x**2+10),x)
[Out]
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GIAC/XCAS [A] time = 0.268994, size = 14, normalized size = 1. \[ \frac{1}{6} \, \arctan \left (\frac{1}{3} \, x^{2} + \frac{1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 10),x, algorithm="giac")
[Out]