\(\int x^{100} \, dx\) [10]

Optimal result

Integrand size = 3, antiderivative size = 7 \[ \int x^{100} \, dx=\frac {x^{101}}{101} \]

[Out]

1/101*x^101

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {30} \[ \int x^{100} \, dx=\frac {x^{101}}{101} \]

[In]

Int[x^100,x]

[Out]

x^101/101

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = \frac {x^{101}}{101} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int x^{100} \, dx=\frac {x^{101}}{101} \]

[In]

Integrate[x^100,x]

[Out]

x^101/101

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86

method	result	size
gosper	\(\frac {x^{101}}{101}\)	\(6\)
default	\(\frac {x^{101}}{101}\)	\(6\)
risch	\(\frac {x^{101}}{101}\)	\(6\)
parallelrisch	\(\frac {x^{101}}{101}\)	\(6\)

[In]

int(x^100,x,method=_RETURNVERBOSE)

[Out]

1/101*x^101

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^{100} \, dx=\frac {1}{101} \, x^{101} \]

[In]

integrate(x^100,x, algorithm="fricas")

[Out]

1/101*x^101

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.43 \[ \int x^{100} \, dx=\frac {x^{101}}{101} \]

[In]

integrate(x**100,x)

[Out]

x**101/101

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^{100} \, dx=\frac {1}{101} \, x^{101} \]

[In]

integrate(x^100,x, algorithm="maxima")

[Out]

1/101*x^101

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^{100} \, dx=\frac {1}{101} \, x^{101} \]

[In]

integrate(x^100,x, algorithm="giac")

[Out]

1/101*x^101

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^{100} \, dx=\frac {x^{101}}{101} \]

[In]

int(x^100,x)

[Out]

x^101/101