3.10 \(\int x^{100} \, dx\)

Optimal. Leaf size=7 \[ \frac {x^{101}}{101} \]

[Out]

1/101*x^101

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {30} \[ \frac {x^{101}}{101} \]

Antiderivative was successfully verified.

[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*} \int x^{100} \, dx &=\frac {x^{101}}{101}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 1.00 \[ \frac {x^{101}}{101} \]

Antiderivative was successfully verified.

[In]

Integrate[x^100,x]

[Out]

x^101/101

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fricas [A]  time = 0.34, size = 5, normalized size = 0.71 \[ \frac {1}{101} x^{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/101*x^101

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giac [A]  time = 1.18, size = 5, normalized size = 0.71 \[ \frac {1}{101} \, x^{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^100,x, algorithm="giac")

[Out]

1/101*x^101

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maple [A]  time = 0.00, size = 6, normalized size = 0.86 \[ \frac {x^{101}}{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^100,x)

[Out]

1/101*x^101

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maxima [A]  time = 0.42, size = 5, normalized size = 0.71 \[ \frac {1}{101} \, x^{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/101*x^101

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mupad [B]  time = 0.12, size = 5, normalized size = 0.71 \[ \frac {x^{101}}{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^100,x)

[Out]

x^101/101

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sympy [A]  time = 0.06, size = 3, normalized size = 0.43 \[ \frac {x^{101}}{101} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**100,x)

[Out]

x**101/101

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