3.1.25 \(\int \frac {1}{x^{5/2}} \, dx\) [25]

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

[Out]

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

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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 {2}{3 x^{3/2}} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} -\frac {2}{3 x^{3/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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

method	result	size
gosper	\(-\frac {2}{3 x^{\frac {3}{2}}}\)	\(6\)
derivativedivides	\(-\frac {2}{3 x^{\frac {3}{2}}}\)	\(6\)
default	\(-\frac {2}{3 x^{\frac {3}{2}}}\)	\(6\)
trager	\(-\frac {2}{3 x^{\frac {3}{2}}}\)	\(6\)
risch	\(-\frac {2}{3 x^{\frac {3}{2}}}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(5/2),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.33, size = 5, normalized size = 0.56 \begin {gather*} -\frac {2}{3 \, x^{\frac {3}{2}}} \end {gather*}

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 = 0.91, size = 5, normalized size = 0.56 \begin {gather*} -\frac {2}{3 \, x^{\frac {3}{2}}} \end {gather*}

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 = 0.02, size = 8, normalized size = 0.89 \begin {gather*} - \frac {2}{3 x^{\frac {3}{2}}} \end {gather*}

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 = 2.30, size = 5, normalized size = 0.56 \begin {gather*} -\frac {2}{3 \, x^{\frac {3}{2}}} \end {gather*}

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)

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Mupad [B]
time = 0.03, size = 5, normalized size = 0.56 \begin {gather*} -\frac {2}{3\,x^{3/2}} \end {gather*}

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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