3.480 \(\int (-1+5 x) \left (-1-x+x^2\right )^2 \, dx\)

Optimal. Leaf size=39 \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]

[Out]

-x + (3*x^2)/2 + (11*x^3)/3 - (3*x^4)/4 - (11*x^5)/5 + (5*x^6)/6

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Rubi [A]  time = 0.035186, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]

Antiderivative was successfully verified.

[In]  Int[(-1 + 5*x)*(-1 - x + x^2)^2,x]

[Out]

-x + (3*x^2)/2 + (11*x^3)/3 - (3*x^4)/4 - (11*x^5)/5 + (5*x^6)/6

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{5 x^{6}}{6} - \frac{11 x^{5}}{5} - \frac{3 x^{4}}{4} + \frac{11 x^{3}}{3} - x + 3 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-1+5*x)*(x**2-x-1)**2,x)

[Out]

5*x**6/6 - 11*x**5/5 - 3*x**4/4 + 11*x**3/3 - x + 3*Integral(x, x)

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Mathematica [A]  time = 0.00247187, size = 39, normalized size = 1. \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]

Antiderivative was successfully verified.

[In]  Integrate[(-1 + 5*x)*(-1 - x + x^2)^2,x]

[Out]

-x + (3*x^2)/2 + (11*x^3)/3 - (3*x^4)/4 - (11*x^5)/5 + (5*x^6)/6

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Maple [A]  time = 0.003, size = 30, normalized size = 0.8 \[ -x+{\frac{3\,{x}^{2}}{2}}+{\frac{11\,{x}^{3}}{3}}-{\frac{3\,{x}^{4}}{4}}-{\frac{11\,{x}^{5}}{5}}+{\frac{5\,{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-1+5*x)*(x^2-x-1)^2,x)

[Out]

-x+3/2*x^2+11/3*x^3-3/4*x^4-11/5*x^5+5/6*x^6

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Maxima [A]  time = 1.76693, size = 39, normalized size = 1. \[ \frac{5}{6} \, x^{6} - \frac{11}{5} \, x^{5} - \frac{3}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{3}{2} \, x^{2} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - x - 1)^2*(5*x - 1),x, algorithm="maxima")

[Out]

5/6*x^6 - 11/5*x^5 - 3/4*x^4 + 11/3*x^3 + 3/2*x^2 - x

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Fricas [A]  time = 0.176109, size = 1, normalized size = 0.03 \[ \frac{5}{6} x^{6} - \frac{11}{5} x^{5} - \frac{3}{4} x^{4} + \frac{11}{3} x^{3} + \frac{3}{2} x^{2} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - x - 1)^2*(5*x - 1),x, algorithm="fricas")

[Out]

5/6*x^6 - 11/5*x^5 - 3/4*x^4 + 11/3*x^3 + 3/2*x^2 - x

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Sympy [A]  time = 0.042663, size = 34, normalized size = 0.87 \[ \frac{5 x^{6}}{6} - \frac{11 x^{5}}{5} - \frac{3 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{3 x^{2}}{2} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-1+5*x)*(x**2-x-1)**2,x)

[Out]

5*x**6/6 - 11*x**5/5 - 3*x**4/4 + 11*x**3/3 + 3*x**2/2 - x

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GIAC/XCAS [A]  time = 0.200296, size = 39, normalized size = 1. \[ \frac{5}{6} \, x^{6} - \frac{11}{5} \, x^{5} - \frac{3}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{3}{2} \, x^{2} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - x - 1)^2*(5*x - 1),x, algorithm="giac")

[Out]

5/6*x^6 - 11/5*x^5 - 3/4*x^4 + 11/3*x^3 + 3/2*x^2 - x