Optimal. Leaf size=49 \[ -\frac{1}{18 \sqrt{x^6+2} x^9}+\frac{x^3}{9 \sqrt{x^6+2}}+\frac{1}{9 \sqrt{x^6+2} x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.036567, antiderivative size = 49, 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 \[ -\frac{1}{18 \sqrt{x^6+2} x^9}+\frac{x^3}{9 \sqrt{x^6+2}}+\frac{1}{9 \sqrt{x^6+2} x^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x^10*(2 + x^6)^(3/2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.34828, size = 42, normalized size = 0.86 \[ \frac{x^{3}}{9 \sqrt{x^{6} + 2}} + \frac{1}{9 x^{3} \sqrt{x^{6} + 2}} - \frac{1}{18 x^{9} \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**10/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0165642, size = 28, normalized size = 0.57 \[ \frac{2 x^{12}+2 x^6-1}{18 x^9 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^10*(2 + x^6)^(3/2)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 25, normalized size = 0.5 \[{\frac{2\,{x}^{12}+2\,{x}^{6}-1}{18\,{x}^{9}}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^10/(x^6+2)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43894, size = 50, normalized size = 1.02 \[ \frac{x^{3}}{24 \, \sqrt{x^{6} + 2}} + \frac{\sqrt{x^{6} + 2}}{12 \, x^{3}} - \frac{{\left (x^{6} + 2\right )}^{\frac{3}{2}}}{72 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^10),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.225412, size = 84, normalized size = 1.71 \[ \frac{2 \, x^{6} - 2 \, \sqrt{x^{6} + 2} x^{3} + 1}{18 \,{\left (2 \, x^{24} + 6 \, x^{18} + 4 \, x^{12} -{\left (2 \, x^{21} + 4 \, x^{15} + x^{9}\right )} \sqrt{x^{6} + 2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^10),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 8.89478, size = 70, normalized size = 1.43 \[ \frac{2 x^{12} \sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}} + \frac{2 x^{6} \sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**10/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (x^{6} + 2\right )}^{\frac{3}{2}} x^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^10),x, algorithm="giac")
[Out]