Optimal. Leaf size=40 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0402759, antiderivative size = 40, 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 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Int[x^17/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.51056, size = 32, normalized size = 0.8 \[ \frac{\left (x^{6} + 2\right )^{\frac{3}{2}}}{9} - \frac{4 \sqrt{x^{6} + 2}}{3} - \frac{4}{3 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**17/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0150235, size = 23, normalized size = 0.57 \[ \frac{x^{12}-8 x^6-32}{9 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^17/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 20, normalized size = 0.5 \[{\frac{{x}^{12}-8\,{x}^{6}-32}{9}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^17/(x^6+2)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43212, size = 38, normalized size = 0.95 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{x^{6} + 2} - \frac{4}{3 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215712, size = 26, normalized size = 0.65 \[ \frac{x^{12} - 8 \, x^{6} - 32}{9 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 19.2386, size = 39, normalized size = 0.98 \[ \frac{x^{12}}{9 \sqrt{x^{6} + 2}} - \frac{8 x^{6}}{9 \sqrt{x^{6} + 2}} - \frac{32}{9 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**17/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.2219, size = 38, normalized size = 0.95 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{x^{6} + 2} - \frac{4}{3 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="giac")
[Out]