3.462 \(\int x \left (1-x^3\right )^2 \, dx\)

Optimal. Leaf size=22 \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]

[Out]

x^2/2 - (2*x^5)/5 + x^8/8

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Rubi [A]  time = 0.0204988, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]

Antiderivative was successfully verified.

[In]  Int[x*(1 - x^3)^2,x]

[Out]

x^2/2 - (2*x^5)/5 + x^8/8

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{8}}{8} - \frac{2 x^{5}}{5} + \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(-x**3+1)**2,x)

[Out]

x**8/8 - 2*x**5/5 + Integral(x, x)

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Mathematica [A]  time = 0.00106874, size = 22, normalized size = 1. \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(1 - x^3)^2,x]

[Out]

x^2/2 - (2*x^5)/5 + x^8/8

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Maple [A]  time = 0.001, size = 17, normalized size = 0.8 \[{\frac{{x}^{2}}{2}}-{\frac{2\,{x}^{5}}{5}}+{\frac{{x}^{8}}{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(-x^3+1)^2,x)

[Out]

1/2*x^2-2/5*x^5+1/8*x^8

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Maxima [A]  time = 0.810013, size = 22, normalized size = 1. \[ \frac{1}{8} \, x^{8} - \frac{2}{5} \, x^{5} + \frac{1}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 - 1)^2*x,x, algorithm="maxima")

[Out]

1/8*x^8 - 2/5*x^5 + 1/2*x^2

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Fricas [A]  time = 0.229898, size = 1, normalized size = 0.05 \[ \frac{1}{8} x^{8} - \frac{2}{5} x^{5} + \frac{1}{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 - 1)^2*x,x, algorithm="fricas")

[Out]

1/8*x^8 - 2/5*x^5 + 1/2*x^2

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Sympy [A]  time = 0.064682, size = 15, normalized size = 0.68 \[ \frac{x^{8}}{8} - \frac{2 x^{5}}{5} + \frac{x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(-x**3+1)**2,x)

[Out]

x**8/8 - 2*x**5/5 + x**2/2

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GIAC/XCAS [A]  time = 0.258153, size = 22, normalized size = 1. \[ \frac{1}{8} \, x^{8} - \frac{2}{5} \, x^{5} + \frac{1}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 - 1)^2*x,x, algorithm="giac")

[Out]

1/8*x^8 - 2/5*x^5 + 1/2*x^2