Optimal. Leaf size=73 \[ \frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{7} a f x^7+\frac{1}{8} b c x^8+\frac{1}{9} b d x^9+\frac{1}{10} b e x^{10}+\frac{1}{11} b f x^{11} \]
[Out]
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Rubi [A] time = 0.125718, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{7} a f x^7+\frac{1}{8} b c x^8+\frac{1}{9} b d x^9+\frac{1}{10} b e x^{10}+\frac{1}{11} b f x^{11} \]
Antiderivative was successfully verified.
[In] Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]
[Out]
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Rubi in Sympy [A] time = 17.9902, size = 66, normalized size = 0.9 \[ \frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{a f x^{7}}{7} + \frac{b c x^{8}}{8} + \frac{b d x^{9}}{9} + \frac{b e x^{10}}{10} + \frac{b f x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)
[Out]
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Mathematica [A] time = 0.0045108, size = 73, normalized size = 1. \[ \frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{7} a f x^7+\frac{1}{8} b c x^8+\frac{1}{9} b d x^9+\frac{1}{10} b e x^{10}+\frac{1}{11} b f x^{11} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 58, normalized size = 0.8 \[{\frac{ac{x}^{4}}{4}}+{\frac{ad{x}^{5}}{5}}+{\frac{ae{x}^{6}}{6}}+{\frac{af{x}^{7}}{7}}+{\frac{bc{x}^{8}}{8}}+{\frac{bd{x}^{9}}{9}}+{\frac{be{x}^{10}}{10}}+{\frac{bf{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x)
[Out]
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Maxima [A] time = 1.37417, size = 77, normalized size = 1.05 \[ \frac{1}{11} \, b f x^{11} + \frac{1}{10} \, b e x^{10} + \frac{1}{9} \, b d x^{9} + \frac{1}{8} \, b c x^{8} + \frac{1}{7} \, a f x^{7} + \frac{1}{6} \, a e x^{6} + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4} \]
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^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191768, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} f b + \frac{1}{10} x^{10} e b + \frac{1}{9} x^{9} d b + \frac{1}{8} x^{8} c b + \frac{1}{7} x^{7} f a + \frac{1}{6} x^{6} e a + \frac{1}{5} x^{5} d a + \frac{1}{4} x^{4} c a \]
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^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.059197, size = 66, normalized size = 0.9 \[ \frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{a f x^{7}}{7} + \frac{b c x^{8}}{8} + \frac{b d x^{9}}{9} + \frac{b e x^{10}}{10} + \frac{b f x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)
[Out]
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GIAC/XCAS [A] time = 0.222835, size = 80, normalized size = 1.1 \[ \frac{1}{11} \, b f x^{11} + \frac{1}{10} \, b x^{10} e + \frac{1}{9} \, b d x^{9} + \frac{1}{8} \, b c x^{8} + \frac{1}{7} \, a f x^{7} + \frac{1}{6} \, a x^{6} e + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4} \]
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^3,x, algorithm="giac")
[Out]