3.25 \(\int \frac{1}{x^{5/2}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0003914, 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} \[ -\frac{2}{3 x^{3/2}} \]

Antiderivative was successfully verified.

[In]

Int[x^(-5/2),x]

[Out]

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

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

Mathematica [A]  time = 0.0007702, size = 9, normalized size = 1. \[ -\frac{2}{3 x^{3/2}} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-5/2),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(5/2),x)

[Out]

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

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Maxima [A]  time = 1.02999, size = 7, normalized size = 0.78 \begin{align*} -\frac{2}{3 \, x^{\frac{3}{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 1.56867, size = 19, normalized size = 2.11 \begin{align*} -\frac{2}{3 \, x^{\frac{3}{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0.051968, size = 8, normalized size = 0.89 \begin{align*} - \frac{2}{3 x^{\frac{3}{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**(5/2),x)

[Out]

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

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Giac [A]  time = 1.09085, size = 7, normalized size = 0.78 \begin{align*} -\frac{2}{3 \, x^{\frac{3}{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2),x, algorithm="giac")

[Out]

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