Optimal. Leaf size=41 \[ -\frac{a^3}{x}+\frac{3}{2} a^2 b x^2+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0377094, antiderivative size = 41, 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 \[ -\frac{a^3}{x}+\frac{3}{2} a^2 b x^2+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{x} + 3 a^{2} b \int x\, dx + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00616447, size = 41, normalized size = 1. \[ -\frac{a^3}{x}+\frac{3}{2} a^2 b x^2+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{3}}{x}}+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{\frac{3\,a{b}^{2}{x}^{5}}{5}}+{\frac{{b}^{3}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41588, size = 47, normalized size = 1.15 \[ \frac{1}{8} \, b^{3} x^{8} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.202621, size = 50, normalized size = 1.22 \[ \frac{5 \, b^{3} x^{9} + 24 \, a b^{2} x^{6} + 60 \, a^{2} b x^{3} - 40 \, a^{3}}{40 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.05114, size = 36, normalized size = 0.88 \[ - \frac{a^{3}}{x} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.217225, size = 47, normalized size = 1.15 \[ \frac{1}{8} \, b^{3} x^{8} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^2,x, algorithm="giac")
[Out]