3.1893 \(\int \left (-1+x^5\right ) \, dx\)

Optimal. Leaf size=11 \[ \frac{x^6}{6}-x \]

[Out]

-x + x^6/6

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Rubi [A]  time = 0.00577281, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{x^6}{6}-x \]

Antiderivative was successfully verified.

[In]  Int[-1 + x^5,x]

[Out]

-x + x^6/6

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Rubi in Sympy [A]  time = 1.02438, size = 5, normalized size = 0.45 \[ \frac{x^{6}}{6} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5-1,x)

[Out]

x**6/6 - x

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Mathematica [A]  time = 0.0000547171, size = 11, normalized size = 1. \[ \frac{x^6}{6}-x \]

Antiderivative was successfully verified.

[In]  Integrate[-1 + x^5,x]

[Out]

-x + x^6/6

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Maple [A]  time = 0., size = 10, normalized size = 0.9 \[ -x+{\frac{{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5-1,x)

[Out]

-x+1/6*x^6

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Maxima [A]  time = 1.31669, size = 12, normalized size = 1.09 \[ \frac{1}{6} \, x^{6} - x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - x

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Fricas [A]  time = 0.173576, size = 1, normalized size = 0.09 \[ \frac{1}{6} x^{6} - x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - x

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Sympy [A]  time = 0.0274, size = 5, normalized size = 0.45 \[ \frac{x^{6}}{6} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5-1,x)

[Out]

x**6/6 - x

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GIAC/XCAS [A]  time = 0.235654, size = 12, normalized size = 1.09 \[ \frac{1}{6} \, x^{6} - x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - x