3.33 \(\int \frac{1}{x^{5/3}} \, dx\)

Optimal. Leaf size=9 \[ -\frac{3}{2 x^{2/3}} \]

[Out]

-3/(2*x^(2/3))

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Rubi [A]  time = 0.0004151, 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} \[ -\frac{3}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]

Int[x^(-5/3),x]

[Out]

-3/(2*x^(2/3))

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^{5/3}} \, dx &=-\frac{3}{2 x^{2/3}}\\ \end{align*}

Mathematica [A]  time = 0.0008142, size = 9, normalized size = 1. \[ -\frac{3}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-5/3),x]

[Out]

-3/(2*x^(2/3))

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Maple [A]  time = 0.002, size = 6, normalized size = 0.7 \begin{align*} -{\frac{3}{2}{x}^{-{\frac{2}{3}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(5/3),x)

[Out]

-3/2/x^(2/3)

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Maxima [A]  time = 0.98278, size = 7, normalized size = 0.78 \begin{align*} -\frac{3}{2 \, x^{\frac{2}{3}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/3),x, algorithm="maxima")

[Out]

-3/2/x^(2/3)

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Fricas [A]  time = 1.58644, size = 19, normalized size = 2.11 \begin{align*} -\frac{3}{2 \, x^{\frac{2}{3}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/3),x, algorithm="fricas")

[Out]

-3/2/x^(2/3)

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Sympy [A]  time = 0.051818, size = 8, normalized size = 0.89 \begin{align*} - \frac{3}{2 x^{\frac{2}{3}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**(5/3),x)

[Out]

-3/(2*x**(2/3))

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Giac [A]  time = 1.19723, size = 7, normalized size = 0.78 \begin{align*} -\frac{3}{2 \, x^{\frac{2}{3}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/3),x, algorithm="giac")

[Out]

-3/2/x^(2/3)