Optimal. Leaf size=44 \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
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Rubi [A] time = 0.0937774, antiderivative size = 44, 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 \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^2*(a + b*x)*(1 - x + x^2)^2,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a x^{7}}{7} + \frac{a x^{4}}{2} + \frac{b x^{8}}{8} + \frac{2 b x^{5}}{5} + b \int x\, dx + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**2*(b*x+a)*(x**2-x+1)**2,x)
[Out]
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Mathematica [A] time = 0.0029928, size = 44, normalized size = 1. \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)^2*(a + b*x)*(1 - x + x^2)^2,x]
[Out]
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Maple [A] time = 0.001, size = 35, normalized size = 0.8 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{a{x}^{4}}{2}}+{\frac{2\,b{x}^{5}}{5}}+{\frac{a{x}^{7}}{7}}+{\frac{b{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^2*(b*x+a)*(x^2-x+1)^2,x)
[Out]
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Maxima [A] time = 0.685829, size = 46, normalized size = 1.05 \[ \frac{1}{8} \, b x^{8} + \frac{1}{7} \, a x^{7} + \frac{2}{5} \, b x^{5} + \frac{1}{2} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^2*(x + 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236192, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} b + \frac{1}{7} x^{7} a + \frac{2}{5} x^{5} b + \frac{1}{2} x^{4} a + \frac{1}{2} x^{2} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^2*(x + 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.098804, size = 37, normalized size = 0.84 \[ \frac{a x^{7}}{7} + \frac{a x^{4}}{2} + a x + \frac{b x^{8}}{8} + \frac{2 b x^{5}}{5} + \frac{b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)**2*(b*x+a)*(x**2-x+1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.256314, size = 46, normalized size = 1.05 \[ \frac{1}{8} \, b x^{8} + \frac{1}{7} \, a x^{7} + \frac{2}{5} \, b x^{5} + \frac{1}{2} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)^2*(x + 1)^2,x, algorithm="giac")
[Out]