Optimal. Leaf size=23 \[ \frac{2 \tan ^{-1}\left (\frac{2 x^3+1}{\sqrt{7}}\right )}{3 \sqrt{7}} \]
[Out]
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Rubi [A] time = 0.0488604, antiderivative size = 23, 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 \[ \frac{2 \tan ^{-1}\left (\frac{2 x^3+1}{\sqrt{7}}\right )}{3 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(2 + x^3 + x^6),x]
[Out]
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Rubi in Sympy [A] time = 5.27161, size = 24, normalized size = 1.04 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\sqrt{7} \left (\frac{2 x^{3}}{7} + \frac{1}{7}\right ) \right )}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**6+x**3+2),x)
[Out]
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Mathematica [A] time = 0.013718, size = 23, normalized size = 1. \[ \frac{2 \tan ^{-1}\left (\frac{2 x^3+1}{\sqrt{7}}\right )}{3 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(2 + x^3 + x^6),x]
[Out]
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Maple [A] time = 0.004, size = 19, normalized size = 0.8 \[{\frac{2\,\sqrt{7}}{21}\arctan \left ({\frac{ \left ( 2\,{x}^{3}+1 \right ) \sqrt{7}}{7}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^6+x^3+2),x)
[Out]
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Maxima [A] time = 0.84682, size = 24, normalized size = 1.04 \[ \frac{2}{21} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{3} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + x^3 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.255343, size = 24, normalized size = 1.04 \[ \frac{2}{21} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{3} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + x^3 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.238163, size = 27, normalized size = 1.17 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\frac{2 \sqrt{7} x^{3}}{7} + \frac{\sqrt{7}}{7} \right )}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**6+x**3+2),x)
[Out]
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GIAC/XCAS [A] time = 0.28272, size = 24, normalized size = 1.04 \[ \frac{2}{21} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{3} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + x^3 + 2),x, algorithm="giac")
[Out]