Optimal. Leaf size=21 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right )}{2 \sqrt{6}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0201487, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right )}{2 \sqrt{6}} \]
Antiderivative was successfully verified.
[In] Int[x/(2 + 3*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.6205, size = 17, normalized size = 0.81 \[ \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(3*x**4+2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0129919, size = 21, normalized size = 1. \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right )}{2 \sqrt{6}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(2 + 3*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 0.7 \[{\frac{\sqrt{6}}{12}\arctan \left ({\frac{{x}^{2}\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(3*x^4+2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.59247, size = 19, normalized size = 0.9 \[ \frac{1}{12} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(3*x^4 + 2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.222981, size = 19, normalized size = 0.9 \[ \frac{1}{12} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(3*x^4 + 2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.189759, size = 17, normalized size = 0.81 \[ \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(3*x**4+2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.224629, size = 19, normalized size = 0.9 \[ \frac{1}{12} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(3*x^4 + 2),x, algorithm="giac")
[Out]