Optimal. Leaf size=50 \[ a^2 A x+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{10} b^2 B x^{10} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.070188, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ a^2 A x+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{10} b^2 B x^{10} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{B b^{2} x^{10}}{10} + a^{2} \int A\, dx + \frac{a x^{4} \left (2 A b + B a\right )}{4} + \frac{b x^{7} \left (A b + 2 B a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0146117, size = 50, normalized size = 1. \[ a^2 A x+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{10} b^2 B x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 49, normalized size = 1. \[{\frac{{b}^{2}B{x}^{10}}{10}}+{\frac{ \left ({b}^{2}A+2\,abB \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{4}}{4}}+{a}^{2}Ax \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36998, size = 65, normalized size = 1.3 \[ \frac{1}{10} \, B b^{2} x^{10} + \frac{1}{7} \,{\left (2 \, B a b + A b^{2}\right )} x^{7} + \frac{1}{4} \,{\left (B a^{2} + 2 \, A a b\right )} x^{4} + A a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.19743, size = 1, normalized size = 0.02 \[ \frac{1}{10} x^{10} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + x a^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.104109, size = 51, normalized size = 1.02 \[ A a^{2} x + \frac{B b^{2} x^{10}}{10} + x^{7} \left (\frac{A b^{2}}{7} + \frac{2 B a b}{7}\right ) + x^{4} \left (\frac{A a b}{2} + \frac{B a^{2}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220903, size = 68, normalized size = 1.36 \[ \frac{1}{10} \, B b^{2} x^{10} + \frac{2}{7} \, B a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + A a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2,x, algorithm="giac")
[Out]