Optimal. Leaf size=40 \[ \frac{2}{15} \left (x^3+1\right )^{5/2}-\frac{4}{9} \left (x^3+1\right )^{3/2}+\frac{2 \sqrt{x^3+1}}{3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0423354, 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 \[ \frac{2}{15} \left (x^3+1\right )^{5/2}-\frac{4}{9} \left (x^3+1\right )^{3/2}+\frac{2 \sqrt{x^3+1}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^8/Sqrt[1 + x^3],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.17593, size = 34, normalized size = 0.85 \[ \frac{2 \left (x^{3} + 1\right )^{\frac{5}{2}}}{15} - \frac{4 \left (x^{3} + 1\right )^{\frac{3}{2}}}{9} + \frac{2 \sqrt{x^{3} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(x**3+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0130601, size = 25, normalized size = 0.62 \[ \frac{2}{45} \sqrt{x^3+1} \left (3 x^6-4 x^3+8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^8/Sqrt[1 + x^3],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 33, normalized size = 0.8 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) \left ( 3\,{x}^{6}-4\,{x}^{3}+8 \right ) }{45}{\frac{1}{\sqrt{{x}^{3}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(x^3+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43205, size = 38, normalized size = 0.95 \[ \frac{2}{15} \,{\left (x^{3} + 1\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{3} + 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(x^3 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.220791, size = 28, normalized size = 0.7 \[ \frac{2}{45} \,{\left (3 \, x^{6} - 4 \, x^{3} + 8\right )} \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(x^3 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.91906, size = 41, normalized size = 1.02 \[ \frac{2 x^{6} \sqrt{x^{3} + 1}}{15} - \frac{8 x^{3} \sqrt{x^{3} + 1}}{45} + \frac{16 \sqrt{x^{3} + 1}}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(x**3+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223494, size = 38, normalized size = 0.95 \[ \frac{2}{15} \,{\left (x^{3} + 1\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{3} + 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(x^3 + 1),x, algorithm="giac")
[Out]