Optimal. Leaf size=27 \[ \frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0303273, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Int[x^11/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.67452, size = 20, normalized size = 0.74 \[ \frac{\sqrt{x^{6} + 2}}{3} + \frac{2}{3 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0105169, size = 18, normalized size = 0.67 \[ \frac{x^6+4}{3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 15, normalized size = 0.6 \[{\frac{{x}^{6}+4}{3}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(x^6+2)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44236, size = 26, normalized size = 0.96 \[ \frac{1}{3} \, \sqrt{x^{6} + 2} + \frac{2}{3 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^6 + 2)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219009, size = 19, normalized size = 0.7 \[ \frac{x^{6} + 4}{3 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^6 + 2)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.64897, size = 24, normalized size = 0.89 \[ \frac{x^{6}}{3 \sqrt{x^{6} + 2}} + \frac{4}{3 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220907, size = 26, normalized size = 0.96 \[ \frac{1}{3} \, \sqrt{x^{6} + 2} + \frac{2}{3 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^6 + 2)^(3/2),x, algorithm="giac")
[Out]