Optimal. Leaf size=28 \[ \frac{a x^4}{4}+a x+\frac{b x^5}{5}+\frac{b x^2}{2} \]
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Rubi [A] time = 0.0449807, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{a x^4}{4}+a x+\frac{b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)*(a + b*x)*(1 - x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a x^{4}}{4} + \frac{b x^{5}}{5} + b \int x\, dx + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(b*x+a)*(x**2-x+1),x)
[Out]
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Mathematica [A] time = 0.00223604, size = 28, normalized size = 1. \[ \frac{a x^4}{4}+a x+\frac{b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)*(a + b*x)*(1 - x + x^2),x]
[Out]
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Maple [A] time = 0.001, size = 23, normalized size = 0.8 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{a{x}^{4}}{4}}+{\frac{b{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(b*x+a)*(x^2-x+1),x)
[Out]
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Maxima [A] time = 0.691403, size = 30, normalized size = 1.07 \[ \frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)*(x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239475, size = 1, normalized size = 0.04 \[ \frac{1}{5} x^{5} b + \frac{1}{4} x^{4} a + \frac{1}{2} x^{2} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)*(x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.085985, size = 22, normalized size = 0.79 \[ \frac{a x^{4}}{4} + a x + \frac{b x^{5}}{5} + \frac{b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(b*x+a)*(x**2-x+1),x)
[Out]
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GIAC/XCAS [A] time = 0.260113, size = 30, normalized size = 1.07 \[ \frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(x^2 - x + 1)*(x + 1),x, algorithm="giac")
[Out]