3.2156 \(\int \left (3-4 x+x^2\right )^2 \, dx\)

Optimal. Leaf size=28 \[ -\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4 \]

[Out]

(-4*(3 - x)^3)/3 - (3 - x)^5/5 + (-3 + x)^4

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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]

(-4*(3 - x)^3)/3 - (3 - x)^5/5 + (-3 + x)^4

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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]

x**5/5 - 2*x**4 + 22*x**3/3 + 9*x - 24*Integral(x, x)

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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]

9*x - 12*x^2 + (22*x^3)/3 - 2*x^4 + x^5/5

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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]

1/5*x^5-2*x^4+22/3*x^3-12*x^2+9*x

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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]

1/5*x^5 - 2*x^4 + 22/3*x^3 - 12*x^2 + 9*x

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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]

1/5*x^5 - 2*x^4 + 22/3*x^3 - 12*x^2 + 9*x

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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]

x**5/5 - 2*x**4 + 22*x**3/3 - 12*x**2 + 9*x

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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]

1/5*x^5 - 2*x^4 + 22/3*x^3 - 12*x^2 + 9*x