Optimal. Leaf size=30 \[ \frac{a^2 x^3}{3}+\frac{2}{7} a b x^7+\frac{b^2 x^{11}}{11} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0322706, antiderivative size = 30, 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 \[ \frac{a^2 x^3}{3}+\frac{2}{7} a b x^7+\frac{b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.20119, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00155, size = 30, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{2}{7} a b x^7+\frac{b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{x}^{3}{a}^{2}}{3}}+{\frac{2\,ab{x}^{7}}{7}}+{\frac{{b}^{2}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^4+a)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42159, size = 32, normalized size = 1.07 \[ \frac{1}{11} \, b^{2} x^{11} + \frac{2}{7} \, a b x^{7} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.199596, size = 1, normalized size = 0.03 \[ \frac{1}{11} x^{11} b^{2} + \frac{2}{7} x^{7} b a + \frac{1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.084343, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.217998, size = 32, normalized size = 1.07 \[ \frac{1}{11} \, b^{2} x^{11} + \frac{2}{7} \, a b x^{7} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2*x^2,x, algorithm="giac")
[Out]