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

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

[Out]

-x + x^6/6

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Rubi [A]  time = 0.00155, 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., Rules used = {} \[ \frac{x^6}{6}-x \]

Antiderivative was successfully verified.

[In]

Int[-1 + x^5,x]

[Out]

-x + x^6/6

Rubi steps

\begin{align*} \int \left (-1+x^5\right ) \, dx &=-x+\frac{x^6}{6}\\ \end{align*}

Mathematica [A]  time = 0.0000415, 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 \begin{align*} -x+{\frac{{x}^{6}}{6}} \end{align*}

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 = 0.984466, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{6} \, x^{6} - x \end{align*}

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 = 1.69048, size = 18, normalized size = 1.64 \begin{align*} \frac{1}{6} x^{6} - x \end{align*}

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 = 0.048918, size = 5, normalized size = 0.45 \begin{align*} \frac{x^{6}}{6} - x \end{align*}

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 [A]  time = 1.07457, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{6} \, x^{6} - x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5-1,x, algorithm="giac")

[Out]

1/6*x^6 - x