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

Optimal result

Integrand size = 5, antiderivative size = 11 \[ \int \left (-1+x^5\right ) \, dx=-x+\frac {x^6}{6} \]

[Out]

-x+1/6*x^6

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-1+x^5\right ) \, dx=\frac {x^6}{6}-x \]

[In]

Int[-1 + x^5,x]

[Out]

-x + x^6/6

Rubi steps \begin{align*} \text {integral}& = -x+\frac {x^6}{6} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (-1+x^5\right ) \, dx=-x+\frac {x^6}{6} \]

[In]

Integrate[-1 + x^5,x]

[Out]

-x + x^6/6

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

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	\(-x +\frac {1}{6} x^{6}\)	\(10\)
parallelrisch	\(-x +\frac {1}{6} x^{6}\)	\(10\)
parts	\(-x +\frac {1}{6} x^{6}\)	\(10\)

[In]

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

[Out]

1/6*x*(x^5-6)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (-1+x^5\right ) \, dx=\frac {1}{6} \, x^{6} - x \]

[In]

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

[Out]

1/6*x^6 - x

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.45 \[ \int \left (-1+x^5\right ) \, dx=\frac {x^{6}}{6} - x \]

[In]

integrate(x**5-1,x)

[Out]

x**6/6 - x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (-1+x^5\right ) \, dx=\frac {1}{6} \, x^{6} - x \]

[In]

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

[Out]

1/6*x^6 - x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (-1+x^5\right ) \, dx=\frac {1}{6} \, x^{6} - x \]

[In]

integrate(x^5-1,x, algorithm="giac")

[Out]

1/6*x^6 - x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (-1+x^5\right ) \, dx=\frac {x\,\left (x^5-6\right )}{6} \]

[In]

int(x^5 - 1,x)

[Out]

(x*(x^5 - 6))/6