Optimal. Leaf size=28 \[ -\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4 \]
[Out]
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Rubi [A] time = 0.035114, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4 \]
Antiderivative was successfully verified.
[In] Int[(3 - 4*x + x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{5}}{5} - 2 x^{4} + \frac{22 x^{3}}{3} + 9 x - 24 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-4*x+3)**2,x)
[Out]
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Mathematica [A] time = 0.00107098, size = 28, normalized size = 1. \[ \frac{x^5}{5}-2 x^4+\frac{22 x^3}{3}-12 x^2+9 x \]
Antiderivative was successfully verified.
[In] Integrate[(3 - 4*x + x^2)^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.9 \[{\frac{{x}^{5}}{5}}-2\,{x}^{4}+{\frac{22\,{x}^{3}}{3}}-12\,{x}^{2}+9\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-4*x+3)^2,x)
[Out]
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Maxima [A] time = 0.801183, size = 32, normalized size = 1.14 \[ \frac{1}{5} \, x^{5} - 2 \, x^{4} + \frac{22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.173743, size = 1, normalized size = 0.04 \[ \frac{1}{5} x^{5} - 2 x^{4} + \frac{22}{3} x^{3} - 12 x^{2} + 9 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.082079, size = 24, normalized size = 0.86 \[ \frac{x^{5}}{5} - 2 x^{4} + \frac{22 x^{3}}{3} - 12 x^{2} + 9 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-4*x+3)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.202135, size = 32, normalized size = 1.14 \[ \frac{1}{5} \, x^{5} - 2 \, x^{4} + \frac{22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2,x, algorithm="giac")
[Out]