Optimal. Leaf size=37 \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0865103, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In] Int[x^3*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.18964, size = 32, normalized size = 0.86 \[ \frac{A a x^{4}}{4} + \frac{A c x^{6}}{6} + \frac{B a x^{5}}{5} + \frac{B c x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(B*x+A)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00395307, size = 37, normalized size = 1. \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 30, normalized size = 0.8 \[{\frac{aA{x}^{4}}{4}}+{\frac{aB{x}^{5}}{5}}+{\frac{Ac{x}^{6}}{6}}+{\frac{Bc{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(B*x+A)*(c*x^2+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.685902, size = 39, normalized size = 1.05 \[ \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263153, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} a B + \frac{1}{4} x^{4} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.087581, size = 32, normalized size = 0.86 \[ \frac{A a x^{4}}{4} + \frac{A c x^{6}}{6} + \frac{B a x^{5}}{5} + \frac{B c x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(B*x+A)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.266438, size = 39, normalized size = 1.05 \[ \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^3,x, algorithm="giac")
[Out]