Optimal. Leaf size=97 \[ \frac{1}{2} a^2 c x^2+\frac{1}{3} a^2 d x^3+\frac{1}{4} a^2 e x^4+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{1}{8} b^2 c x^8+\frac{1}{9} b^2 d x^9+\frac{1}{10} b^2 e x^{10} \]
[Out]
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Rubi [A] time = 0.145058, antiderivative size = 97, 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 \[ \frac{1}{2} a^2 c x^2+\frac{1}{3} a^2 d x^3+\frac{1}{4} a^2 e x^4+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{1}{8} b^2 c x^8+\frac{1}{9} b^2 d x^9+\frac{1}{10} b^2 e x^{10} \]
Antiderivative was successfully verified.
[In] Int[x*(c + d*x + e*x^2)*(a + b*x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} c \int x\, dx + \frac{a^{2} e x^{4}}{4} + \frac{2 a b c x^{5}}{5} + \frac{2 a b e x^{7}}{7} + \frac{b^{2} c x^{8}}{8} + \frac{b^{2} e x^{10}}{10} + \frac{d \left (a + b x^{3}\right )^{3}}{9 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**2,x)
[Out]
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Mathematica [A] time = 0.00573634, size = 97, normalized size = 1. \[ \frac{1}{2} a^2 c x^2+\frac{1}{3} a^2 d x^3+\frac{1}{4} a^2 e x^4+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{1}{8} b^2 c x^8+\frac{1}{9} b^2 d x^9+\frac{1}{10} b^2 e x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[x*(c + d*x + e*x^2)*(a + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.001, size = 80, normalized size = 0.8 \[{\frac{{a}^{2}c{x}^{2}}{2}}+{\frac{{a}^{2}d{x}^{3}}{3}}+{\frac{{a}^{2}e{x}^{4}}{4}}+{\frac{2\,abc{x}^{5}}{5}}+{\frac{abd{x}^{6}}{3}}+{\frac{2\,abe{x}^{7}}{7}}+{\frac{{b}^{2}c{x}^{8}}{8}}+{\frac{{b}^{2}d{x}^{9}}{9}}+{\frac{{b}^{2}e{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(e*x^2+d*x+c)*(b*x^3+a)^2,x)
[Out]
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Maxima [A] time = 1.37669, size = 107, normalized size = 1.1 \[ \frac{1}{10} \, b^{2} e x^{10} + \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{8} \, b^{2} c x^{8} + \frac{2}{7} \, a b e x^{7} + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} e x^{4} + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{2} \, a^{2} c x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(e*x^2 + d*x + c)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.188728, size = 1, normalized size = 0.01 \[ \frac{1}{10} x^{10} e b^{2} + \frac{1}{9} x^{9} d b^{2} + \frac{1}{8} x^{8} c b^{2} + \frac{2}{7} x^{7} e b a + \frac{1}{3} x^{6} d b a + \frac{2}{5} x^{5} c b a + \frac{1}{4} x^{4} e a^{2} + \frac{1}{3} x^{3} d a^{2} + \frac{1}{2} x^{2} c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(e*x^2 + d*x + c)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.069293, size = 94, normalized size = 0.97 \[ \frac{a^{2} c x^{2}}{2} + \frac{a^{2} d x^{3}}{3} + \frac{a^{2} e x^{4}}{4} + \frac{2 a b c x^{5}}{5} + \frac{a b d x^{6}}{3} + \frac{2 a b e x^{7}}{7} + \frac{b^{2} c x^{8}}{8} + \frac{b^{2} d x^{9}}{9} + \frac{b^{2} e x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208943, size = 111, normalized size = 1.14 \[ \frac{1}{10} \, b^{2} x^{10} e + \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{8} \, b^{2} c x^{8} + \frac{2}{7} \, a b x^{7} e + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} x^{4} e + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{2} \, a^{2} c x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(e*x^2 + d*x + c)*x,x, algorithm="giac")
[Out]