3.251 \(\int \frac{1}{x^{10}} \, dx\)

Optimal. Leaf size=7 \[ -\frac{1}{9 x^9} \]

[Out]

-1/(9*x^9)

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Rubi [A]  time = 0.0004806, 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} \[ -\frac{1}{9 x^9} \]

Antiderivative was successfully verified.

[In]

Int[x^(-10),x]

[Out]

-1/(9*x^9)

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 \frac{1}{x^{10}} \, dx &=-\frac{1}{9 x^9}\\ \end{align*}

Mathematica [A]  time = 0.0001022, size = 7, normalized size = 1. \[ -\frac{1}{9 x^9} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-10),x]

[Out]

-1/(9*x^9)

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Maple [A]  time = 0., size = 6, normalized size = 0.9 \begin{align*} -{\frac{1}{9\,{x}^{9}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^10,x)

[Out]

-1/9/x^9

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Maxima [A]  time = 1.07673, size = 7, normalized size = 1. \begin{align*} -\frac{1}{9 \, x^{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^10,x, algorithm="maxima")

[Out]

-1/9/x^9

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Fricas [A]  time = 1.55583, size = 14, normalized size = 2. \begin{align*} -\frac{1}{9 \, x^{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^10,x, algorithm="fricas")

[Out]

-1/9/x^9

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Sympy [A]  time = 0.070336, size = 7, normalized size = 1. \begin{align*} - \frac{1}{9 x^{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**10,x)

[Out]

-1/(9*x**9)

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Giac [A]  time = 1.20951, size = 7, normalized size = 1. \begin{align*} -\frac{1}{9 \, x^{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^10,x, algorithm="giac")

[Out]

-1/9/x^9