3.1.29 \(\int \sqrt [3]{x} \, dx\) [29]

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

[Out]

3/4*x^(4/3)

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Rubi [A]
time = 0.00, antiderivative size = 9, 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*} \frac {3 x^{4/3}}{4} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {3 x^{4/3}}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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Maple [A]
time = 0.02, size = 6, normalized size = 0.67

method	result	size
gosper	\(\frac {3 x^{\frac {4}{3}}}{4}\)	\(6\)
derivativedivides	\(\frac {3 x^{\frac {4}{3}}}{4}\)	\(6\)
default	\(\frac {3 x^{\frac {4}{3}}}{4}\)	\(6\)
trager	\(\frac {3 x^{\frac {4}{3}}}{4}\)	\(6\)
risch	\(\frac {3 x^{\frac {4}{3}}}{4}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)

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Maxima [A]
time = 0.28, size = 5, normalized size = 0.56 \begin {gather*} \frac {3}{4} \, x^{\frac {4}{3}} \end {gather*}

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 = 0.97, size = 5, normalized size = 0.56 \begin {gather*} \frac {3}{4} \, x^{\frac {4}{3}} \end {gather*}

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 = 0.02, size = 7, normalized size = 0.78 \begin {gather*} \frac {3 x^{\frac {4}{3}}}{4} \end {gather*}

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 = 1.42, size = 5, normalized size = 0.56 \begin {gather*} \frac {3}{4} \, x^{\frac {4}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x^(4/3)

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Mupad [B]
time = 0.06, size = 5, normalized size = 0.56 \begin {gather*} \frac {3\,x^{4/3}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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