Optimal. Leaf size=33 \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.104397, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{B b x^{9}}{9} + \frac{a \int ^{x^{3}} A\, dx}{3} + \left (\frac{A b}{3} + \frac{B a}{3}\right ) \int ^{x^{3}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0153083, size = 33, normalized size = 1. \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 28, normalized size = 0.9 \[{\frac{aA{x}^{3}}{3}}+{\frac{ \left ( Ab+Ba \right ){x}^{6}}{6}}+{\frac{bB{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^3+a)*(B*x^3+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40642, size = 36, normalized size = 1.09 \[ \frac{1}{9} \, B b x^{9} + \frac{1}{6} \,{\left (B a + A b\right )} x^{6} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.20057, size = 1, normalized size = 0.03 \[ \frac{1}{9} x^{9} b B + \frac{1}{6} x^{6} a B + \frac{1}{6} x^{6} b A + \frac{1}{3} x^{3} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.078523, size = 29, normalized size = 0.88 \[ \frac{A a x^{3}}{3} + \frac{B b x^{9}}{9} + x^{6} \left (\frac{A b}{6} + \frac{B a}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.235945, size = 39, normalized size = 1.18 \[ \frac{1}{9} \, B b x^{9} + \frac{1}{6} \, B a x^{6} + \frac{1}{6} \, A b x^{6} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^2,x, algorithm="giac")
[Out]