Optimal. Leaf size=60 \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
[Out]
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Rubi [A] time = 0.113183, antiderivative size = 60, 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 \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^3*(a + b*x)*(1 - x + x^2)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a x^{10}}{10} + \frac{3 a x^{7}}{7} + \frac{3 a x^{4}}{4} + \frac{b x^{11}}{11} + \frac{3 b x^{8}}{8} + \frac{3 b x^{5}}{5} + b \int x\, dx + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**3*(b*x+a)*(x**2-x+1)**3,x)
[Out]
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Mathematica [A] time = 0.0034459, size = 60, normalized size = 1. \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)^3*(a + b*x)*(1 - x + x^2)^3,x]
[Out]
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Maple [A] time = 0.002, size = 47, normalized size = 0.8 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{3\,a{x}^{4}}{4}}+{\frac{3\,b{x}^{5}}{5}}+{\frac{3\,a{x}^{7}}{7}}+{\frac{3\,b{x}^{8}}{8}}+{\frac{a{x}^{10}}{10}}+{\frac{b{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^3*(b*x+a)*(x^2-x+1)^3,x)
[Out]
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Maxima [A] time = 0.685188, size = 62, normalized size = 1.03 \[ \frac{1}{11} \, b x^{11} + \frac{1}{10} \, a x^{10} + \frac{3}{8} \, b x^{8} + \frac{3}{7} \, a x^{7} + \frac{3}{5} \, b x^{5} + \frac{3}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^3*(x + 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23729, size = 1, normalized size = 0.02 \[ \frac{1}{11} x^{11} b + \frac{1}{10} x^{10} a + \frac{3}{8} x^{8} b + \frac{3}{7} x^{7} a + \frac{3}{5} x^{5} b + \frac{3}{4} x^{4} a + \frac{1}{2} x^{2} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^3*(x + 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.117013, size = 56, normalized size = 0.93 \[ \frac{a x^{10}}{10} + \frac{3 a x^{7}}{7} + \frac{3 a x^{4}}{4} + a x + \frac{b x^{11}}{11} + \frac{3 b x^{8}}{8} + \frac{3 b x^{5}}{5} + \frac{b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)**3*(b*x+a)*(x**2-x+1)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.257553, size = 62, normalized size = 1.03 \[ \frac{1}{11} \, b x^{11} + \frac{1}{10} \, a x^{10} + \frac{3}{8} \, b x^{8} + \frac{3}{7} \, a x^{7} + \frac{3}{5} \, b x^{5} + \frac{3}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^3*(x + 1)^3,x, algorithm="giac")
[Out]