3.1.31 \(\int \frac {1}{x^{2/3}} \, dx\) [31]

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

[Out]

3*x^(1/3)

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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 = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {30} \begin {gather*} 3 \sqrt [3]{x} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} 3 \sqrt [3]{x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

3*x^(1/3)

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Maple [A]
time = 0.02, size = 6, normalized size = 0.86

method	result	size
gosper	\(3 x^{\frac {1}{3}}\)	\(6\)
derivativedivides	\(3 x^{\frac {1}{3}}\)	\(6\)
default	\(3 x^{\frac {1}{3}}\)	\(6\)
trager	\(3 x^{\frac {1}{3}}\)	\(6\)
risch	\(3 x^{\frac {1}{3}}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(2/3),x,method=_RETURNVERBOSE)

[Out]

3*x^(1/3)

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Maxima [A]
time = 0.31, size = 5, normalized size = 0.71 \begin {gather*} 3 \, x^{\frac {1}{3}} \end {gather*}

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 = 1.01, size = 5, normalized size = 0.71 \begin {gather*} 3 \, x^{\frac {1}{3}} \end {gather*}

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 = 0.02, size = 5, normalized size = 0.71 \begin {gather*} 3 \sqrt [3]{x} \end {gather*}

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 = 1.71, size = 5, normalized size = 0.71 \begin {gather*} 3 \, x^{\frac {1}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x^(1/3)

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Mupad [B]
time = 0.07, size = 5, normalized size = 0.71 \begin {gather*} 3\,x^{1/3} \end {gather*}

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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