Optimal. Leaf size=25 \[ a^2 x+\frac{2}{5} a b x^5+\frac{b^2 x^9}{9} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0196626, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ a^2 x+\frac{2}{5} a b x^5+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{9}}{9} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00145464, size = 25, normalized size = 1. \[ a^2 x+\frac{2}{5} a b x^5+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 22, normalized size = 0.9 \[ x{a}^{2}+{\frac{2\,{x}^{5}ab}{5}}+{\frac{{b}^{2}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4217, size = 28, normalized size = 1.12 \[ \frac{1}{9} \, b^{2} x^{9} + \frac{2}{5} \, a b x^{5} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205749, size = 1, normalized size = 0.04 \[ \frac{1}{9} x^{9} b^{2} + \frac{2}{5} x^{5} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.082973, size = 22, normalized size = 0.88 \[ a^{2} x + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.218151, size = 28, normalized size = 1.12 \[ \frac{1}{9} \, b^{2} x^{9} + \frac{2}{5} \, a b x^{5} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2,x, algorithm="giac")
[Out]