3.29 \(\int \sqrt [3]{x} \, dx\)

Optimal. Leaf size=9 \[ \frac{3 x^{4/3}}{4} \]

[Out]

(3*x^(4/3))/4

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Rubi [A]  time = 0.0004372, antiderivative size = 9, 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} \[ \frac{3 x^{4/3}}{4} \]

Antiderivative was successfully verified.

[In]

Int[x^(1/3),x]

[Out]

(3*x^(4/3))/4

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 \sqrt [3]{x} \, dx &=\frac{3 x^{4/3}}{4}\\ \end{align*}

Mathematica [A]  time = 0.0024849, size = 9, normalized size = 1. \[ \frac{3 x^{4/3}}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(1/3),x]

[Out]

(3*x^(4/3))/4

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Maple [A]  time = 0.002, size = 6, normalized size = 0.7 \begin{align*}{\frac{3}{4}{x}^{{\frac{4}{3}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)

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Maxima [A]  time = 1.02265, size = 7, normalized size = 0.78 \begin{align*} \frac{3}{4} \, x^{\frac{4}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)

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Fricas [A]  time = 1.53806, size = 18, normalized size = 2. \begin{align*} \frac{3}{4} \, x^{\frac{4}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)

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Sympy [A]  time = 0.051377, size = 7, normalized size = 0.78 \begin{align*} \frac{3 x^{\frac{4}{3}}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x**(4/3)/4

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Giac [A]  time = 1.09591, size = 7, normalized size = 0.78 \begin{align*} \frac{3}{4} \, x^{\frac{4}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)