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

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

[Out]

x^101/101

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Rubi [A]  time = 0.0004215, antiderivative size = 7, normalized size of antiderivative = 1., 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*}

Mathematica [A]  time = 0.0002596, size = 7, normalized size = 1. \[ \frac{x^{101}}{101} \]

Antiderivative was successfully verified.

[In]

Integrate[x^100,x]

[Out]

x^101/101

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Maple [A]  time = 0., size = 6, normalized size = 0.9 \begin{align*}{\frac{{x}^{101}}{101}} \end{align*}

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 = 1.01248, size = 7, normalized size = 1. \begin{align*} \frac{1}{101} \, x^{101} \end{align*}

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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Fricas [A]  time = 1.29079, size = 18, normalized size = 2.57 \begin{align*} \frac{1}{101} x^{101} \end{align*}

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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Sympy [A]  time = 0.048739, size = 3, normalized size = 0.43 \begin{align*} \frac{x^{101}}{101} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**100,x)

[Out]

x**101/101

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Giac [A]  time = 1.09151, size = 7, normalized size = 1. \begin{align*} \frac{1}{101} \, x^{101} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^100,x, algorithm="giac")

[Out]

1/101*x^101