Optimal. Leaf size=55 \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
[Out]
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Rubi [A] time = 0.101293, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
Antiderivative was successfully verified.
[In] Int[x^2*(c + d*x + e*x^2)*(a + b*x^3),x]
[Out]
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Rubi in Sympy [A] time = 13.1799, size = 49, normalized size = 0.89 \[ \frac{a c x^{3}}{3} + \frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b c x^{6}}{6} + \frac{b d x^{7}}{7} + \frac{b e x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a),x)
[Out]
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Mathematica [A] time = 0.00417322, size = 55, normalized size = 1. \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(c + d*x + e*x^2)*(a + b*x^3),x]
[Out]
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Maple [A] time = 0.002, size = 44, normalized size = 0.8 \[{\frac{ac{x}^{3}}{3}}+{\frac{ad{x}^{4}}{4}}+{\frac{ae{x}^{5}}{5}}+{\frac{bc{x}^{6}}{6}}+{\frac{bd{x}^{7}}{7}}+{\frac{be{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(e*x^2+d*x+c)*(b*x^3+a),x)
[Out]
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Maxima [A] time = 1.42165, size = 58, normalized size = 1.05 \[ \frac{1}{8} \, b e x^{8} + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a e x^{5} + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(e*x^2 + d*x + c)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19167, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} e b + \frac{1}{7} x^{7} d b + \frac{1}{6} x^{6} c b + \frac{1}{5} x^{5} e a + \frac{1}{4} x^{4} d a + \frac{1}{3} x^{3} c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(e*x^2 + d*x + c)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.049732, size = 49, normalized size = 0.89 \[ \frac{a c x^{3}}{3} + \frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b c x^{6}}{6} + \frac{b d x^{7}}{7} + \frac{b e x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a),x)
[Out]
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GIAC/XCAS [A] time = 0.210504, size = 61, normalized size = 1.11 \[ \frac{1}{8} \, b x^{8} e + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a x^{5} e + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(e*x^2 + d*x + c)*x^2,x, algorithm="giac")
[Out]