3.31 \(\int \frac{1}{x^{2/3}} \, dx\)

Optimal. Leaf size=7 \[ 3 \sqrt [3]{x} \]

[Out]

3*x^(1/3)

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Rubi [A]  time = 0.0004344, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {30} \[ 3 \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]

Int[x^(-2/3),x]

[Out]

3*x^(1/3)

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^{2/3}} \, dx &=3 \sqrt [3]{x}\\ \end{align*}

Mathematica [A]  time = 0.0007684, size = 7, normalized size = 1. \[ 3 \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-2/3),x]

[Out]

3*x^(1/3)

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Maple [A]  time = 0.001, size = 6, normalized size = 0.9 \begin{align*} 3\,\sqrt [3]{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(2/3),x)

[Out]

3*x^(1/3)

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Maxima [A]  time = 1.03224, size = 7, normalized size = 1. \begin{align*} 3 \, x^{\frac{1}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(2/3),x, algorithm="maxima")

[Out]

3*x^(1/3)

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Fricas [A]  time = 1.4012, size = 15, normalized size = 2.14 \begin{align*} 3 \, x^{\frac{1}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(2/3),x, algorithm="fricas")

[Out]

3*x^(1/3)

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Sympy [A]  time = 0.051347, size = 5, normalized size = 0.71 \begin{align*} 3 \sqrt [3]{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**(2/3),x)

[Out]

3*x**(1/3)

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Giac [A]  time = 1.09975, size = 7, normalized size = 1. \begin{align*} 3 \, x^{\frac{1}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(2/3),x, algorithm="giac")

[Out]

3*x^(1/3)