Optimal. Leaf size=68 \[ a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} a f x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7+\frac{1}{8} b f x^8 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0876593, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} a f x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7+\frac{1}{8} b f x^8 \]
Antiderivative was successfully verified.
[In] Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a d \int x\, dx + \frac{a e x^{3}}{3} + \frac{a f x^{4}}{4} + \frac{b c x^{5}}{5} + \frac{b d x^{6}}{6} + \frac{b e x^{7}}{7} + \frac{b f x^{8}}{8} + c \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00835988, size = 68, normalized size = 1. \[ a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} a f x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7+\frac{1}{8} b f x^8 \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 55, normalized size = 0.8 \[ acx+{\frac{ad{x}^{2}}{2}}+{\frac{ae{x}^{3}}{3}}+{\frac{af{x}^{4}}{4}}+{\frac{bc{x}^{5}}{5}}+{\frac{bd{x}^{6}}{6}}+{\frac{be{x}^{7}}{7}}+{\frac{bf{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((f*x^3+e*x^2+d*x+c)*(b*x^4+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.38915, size = 73, normalized size = 1.07 \[ \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, b e x^{7} + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a f x^{4} + \frac{1}{3} \, a e x^{3} + \frac{1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.186994, size = 1, normalized size = 0.01 \[ \frac{1}{8} x^{8} f b + \frac{1}{7} x^{7} e b + \frac{1}{6} x^{6} d b + \frac{1}{5} x^{5} c b + \frac{1}{4} x^{4} f a + \frac{1}{3} x^{3} e a + \frac{1}{2} x^{2} d a + x c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.05271, size = 63, normalized size = 0.93 \[ a c x + \frac{a d x^{2}}{2} + \frac{a e x^{3}}{3} + \frac{a f x^{4}}{4} + \frac{b c x^{5}}{5} + \frac{b d x^{6}}{6} + \frac{b e x^{7}}{7} + \frac{b f x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.214752, size = 76, normalized size = 1.12 \[ \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a f x^{4} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c),x, algorithm="giac")
[Out]