Optimal. Leaf size=93 \[ \frac{1}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.207684, antiderivative size = 93, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{1}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
[In] Int[x^3*(A + B*x)*(a + c*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 15.9174, size = 90, normalized size = 0.97 \[ \frac{A a^{3} x^{4}}{4} + \frac{A a^{2} c x^{6}}{2} + \frac{3 A a c^{2} x^{8}}{8} + \frac{A c^{3} x^{10}}{10} + \frac{B a^{3} x^{5}}{5} + \frac{3 B a^{2} c x^{7}}{7} + \frac{B a c^{2} x^{9}}{3} + \frac{B c^{3} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(B*x+A)*(c*x**2+a)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00578753, size = 93, normalized size = 1. \[ \frac{1}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(A + B*x)*(a + c*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 78, normalized size = 0.8 \[{\frac{{a}^{3}A{x}^{4}}{4}}+{\frac{{a}^{3}B{x}^{5}}{5}}+{\frac{{a}^{2}Ac{x}^{6}}{2}}+{\frac{3\,{a}^{2}Bc{x}^{7}}{7}}+{\frac{3\,aA{c}^{2}{x}^{8}}{8}}+{\frac{aB{c}^{2}{x}^{9}}{3}}+{\frac{A{c}^{3}{x}^{10}}{10}}+{\frac{B{c}^{3}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(B*x+A)*(c*x^2+a)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.691677, size = 104, normalized size = 1.12 \[ \frac{1}{11} \, B c^{3} x^{11} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.261666, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} c^{3} B + \frac{1}{10} x^{10} c^{3} A + \frac{1}{3} x^{9} c^{2} a B + \frac{3}{8} x^{8} c^{2} a A + \frac{3}{7} x^{7} c a^{2} B + \frac{1}{2} x^{6} c a^{2} A + \frac{1}{5} x^{5} a^{3} B + \frac{1}{4} x^{4} a^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.126461, size = 90, normalized size = 0.97 \[ \frac{A a^{3} x^{4}}{4} + \frac{A a^{2} c x^{6}}{2} + \frac{3 A a c^{2} x^{8}}{8} + \frac{A c^{3} x^{10}}{10} + \frac{B a^{3} x^{5}}{5} + \frac{3 B a^{2} c x^{7}}{7} + \frac{B a c^{2} x^{9}}{3} + \frac{B c^{3} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(B*x+A)*(c*x**2+a)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.266828, size = 104, normalized size = 1.12 \[ \frac{1}{11} \, B c^{3} x^{11} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^3,x, algorithm="giac")
[Out]