Optimal. Leaf size=43 \[ \frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.072255, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
Antiderivative was successfully verified.
[In] Int[x^11*(a + b*x^3)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.84814, size = 36, normalized size = 0.84 \[ \frac{a^{3} x^{12}}{12} + \frac{a^{2} b x^{15}}{5} + \frac{a b^{2} x^{18}}{6} + \frac{b^{3} x^{21}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11*(b*x**3+a)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00312111, size = 43, normalized size = 1. \[ \frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
Antiderivative was successfully verified.
[In] Integrate[x^11*(a + b*x^3)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{12}}{12}}+{\frac{{a}^{2}b{x}^{15}}{5}}+{\frac{a{b}^{2}{x}^{18}}{6}}+{\frac{{b}^{3}{x}^{21}}{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11*(b*x^3+a)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4392, size = 47, normalized size = 1.09 \[ \frac{1}{21} \, b^{3} x^{21} + \frac{1}{6} \, a b^{2} x^{18} + \frac{1}{5} \, a^{2} b x^{15} + \frac{1}{12} \, a^{3} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^11,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.19088, size = 1, normalized size = 0.02 \[ \frac{1}{21} x^{21} b^{3} + \frac{1}{6} x^{18} b^{2} a + \frac{1}{5} x^{15} b a^{2} + \frac{1}{12} x^{12} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^11,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.098185, size = 36, normalized size = 0.84 \[ \frac{a^{3} x^{12}}{12} + \frac{a^{2} b x^{15}}{5} + \frac{a b^{2} x^{18}}{6} + \frac{b^{3} x^{21}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11*(b*x**3+a)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220302, size = 47, normalized size = 1.09 \[ \frac{1}{21} \, b^{3} x^{21} + \frac{1}{6} \, a b^{2} x^{18} + \frac{1}{5} \, a^{2} b x^{15} + \frac{1}{12} \, a^{3} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^11,x, algorithm="giac")
[Out]