3.1899 \(\int \left (-2 x+x^2+x^3\right ) \, dx\)

Optimal. Leaf size=20 \[ \frac{x^4}{4}+\frac{x^3}{3}-x^2 \]

[Out]

-x^2 + x^3/3 + x^4/4

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Rubi [A]  time = 0.00848915, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{x^4}{4}+\frac{x^3}{3}-x^2 \]

Antiderivative was successfully verified.

[In]  Int[-2*x + x^2 + x^3,x]

[Out]

-x^2 + x^3/3 + x^4/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{4}}{4} + \frac{x^{3}}{3} - 2 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3+x**2-2*x,x)

[Out]

x**4/4 + x**3/3 - 2*Integral(x, x)

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Mathematica [A]  time = 0.0000604768, size = 20, normalized size = 1. \[ \frac{x^4}{4}+\frac{x^3}{3}-x^2 \]

Antiderivative was successfully verified.

[In]  Integrate[-2*x + x^2 + x^3,x]

[Out]

-x^2 + x^3/3 + x^4/4

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Maple [A]  time = 0., size = 17, normalized size = 0.9 \[ -{x}^{2}+{\frac{{x}^{3}}{3}}+{\frac{{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3+x^2-2*x,x)

[Out]

-x^2+1/3*x^3+1/4*x^4

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Maxima [A]  time = 1.32148, size = 22, normalized size = 1.1 \[ \frac{1}{4} \, x^{4} + \frac{1}{3} \, x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3 + x^2 - 2*x,x, algorithm="maxima")

[Out]

1/4*x^4 + 1/3*x^3 - x^2

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Fricas [A]  time = 0.176844, size = 1, normalized size = 0.05 \[ \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3 + x^2 - 2*x,x, algorithm="fricas")

[Out]

1/4*x^4 + 1/3*x^3 - x^2

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Sympy [A]  time = 0.028754, size = 12, normalized size = 0.6 \[ \frac{x^{4}}{4} + \frac{x^{3}}{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3+x**2-2*x,x)

[Out]

x**4/4 + x**3/3 - x**2

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GIAC/XCAS [A]  time = 0.229173, size = 22, normalized size = 1.1 \[ \frac{1}{4} \, x^{4} + \frac{1}{3} \, x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3 + x^2 - 2*x,x, algorithm="giac")

[Out]

1/4*x^4 + 1/3*x^3 - x^2