Optimal. Leaf size=32 \[ \frac{x^7}{7}-\frac{4 x^6}{3}+\frac{22 x^5}{5}-6 x^4+3 x^3 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0378095, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{x^7}{7}-\frac{4 x^6}{3}+\frac{22 x^5}{5}-6 x^4+3 x^3 \]
Antiderivative was successfully verified.
[In] Int[x^2*(3 - 4*x + x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.74129, size = 27, normalized size = 0.84 \[ \frac{x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{22 x^{5}}{5} - 6 x^{4} + 3 x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(x**2-4*x+3)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00174647, size = 32, normalized size = 1. \[ \frac{x^7}{7}-\frac{4 x^6}{3}+\frac{22 x^5}{5}-6 x^4+3 x^3 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(3 - 4*x + x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 27, normalized size = 0.8 \[ 3\,{x}^{3}-6\,{x}^{4}+{\frac{22\,{x}^{5}}{5}}-{\frac{4\,{x}^{6}}{3}}+{\frac{{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(x^2-4*x+3)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.820962, size = 35, normalized size = 1.09 \[ \frac{1}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.17829, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} - \frac{4}{3} x^{6} + \frac{22}{5} x^{5} - 6 x^{4} + 3 x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.084502, size = 27, normalized size = 0.84 \[ \frac{x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{22 x^{5}}{5} - 6 x^{4} + 3 x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(x**2-4*x+3)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.202545, size = 35, normalized size = 1.09 \[ \frac{1}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2*x^2,x, algorithm="giac")
[Out]