3.19.93 \(\int (-1+x^5) \, dx\) [1893]

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

[Out]

-x+1/6*x^6

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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^6}{6}-x \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -x+\frac {x^6}{6} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + x^5,x]

[Out]

-x + x^6/6

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Maple [A]
time = 0.01, size = 10, normalized size = 0.91

method	result	size
gosper	\(\frac {x \left (x^{5}-6\right )}{6}\)	\(9\)
default	\(-x +\frac {1}{6} x^{6}\)	\(10\)
norman	\(-x +\frac {1}{6} x^{6}\)	\(10\)
risch	\(-x +\frac {1}{6} x^{6}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5-1,x,method=_RETURNVERBOSE)

[Out]

-x+1/6*x^6

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Maxima [A]
time = 0.28, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{6} \, x^{6} - x \end {gather*}

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 = 0.60, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{6} \, x^{6} - x \end {gather*}

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 = 0.00, size = 5, normalized size = 0.45 \begin {gather*} \frac {x^{6}}{6} - x \end {gather*}

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 = 1.51, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{6} \, x^{6} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5-1,x, algorithm="giac")

[Out]

1/6*x^6 - x

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Mupad [B]
time = 0.02, size = 8, normalized size = 0.73 \begin {gather*} \frac {x\,\left (x^5-6\right )}{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5 - 1,x)

[Out]

(x*(x^5 - 6))/6

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