Optimal. Leaf size=22 \[ \frac{x^7}{7}-\frac{8 x^5}{5}+\frac{16 x^3}{3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0237059, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{x^7}{7}-\frac{8 x^5}{5}+\frac{16 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[x^2*(4 - x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.29155, size = 17, normalized size = 0.77 \[ \frac{x^{7}}{7} - \frac{8 x^{5}}{5} + \frac{16 x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(-x**2+4)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00120954, size = 22, normalized size = 1. \[ \frac{x^7}{7}-\frac{8 x^5}{5}+\frac{16 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(4 - x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 17, normalized size = 0.8 \[{\frac{16\,{x}^{3}}{3}}-{\frac{8\,{x}^{5}}{5}}+{\frac{{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(-x^2+4)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.817242, size = 22, normalized size = 1. \[ \frac{1}{7} \, x^{7} - \frac{8}{5} \, x^{5} + \frac{16}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4)^2*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.236009, size = 1, normalized size = 0.05 \[ \frac{1}{7} x^{7} - \frac{8}{5} x^{5} + \frac{16}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4)^2*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.067429, size = 17, normalized size = 0.77 \[ \frac{x^{7}}{7} - \frac{8 x^{5}}{5} + \frac{16 x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(-x**2+4)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.259366, size = 22, normalized size = 1. \[ \frac{1}{7} \, x^{7} - \frac{8}{5} \, x^{5} + \frac{16}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4)^2*x^2,x, algorithm="giac")
[Out]