3.1.20 \(\int x^{5/2} \, dx\) [20]

Optimal. Leaf size=9 \[ \frac {2 x^{7/2}}{7} \]

[Out]

2/7*x^(7/2)

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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 x^{7/2}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*x^(7/2))/7

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 x^{5/2} \, dx &=\frac {2 x^{7/2}}{7}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {2 x^{7/2}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*x^(7/2))/7

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Mathics [A]
time = 1.52, size = 5, normalized size = 0.56 \begin {gather*} \frac {2 x^{\frac {7}{2}}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[x^(5/2),x]')

[Out]

2 x ^ (7 / 2) / 7

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

method	result	size
gosper	\(\frac {2 x^{\frac {7}{2}}}{7}\)	\(6\)
derivativedivides	\(\frac {2 x^{\frac {7}{2}}}{7}\)	\(6\)
default	\(\frac {2 x^{\frac {7}{2}}}{7}\)	\(6\)
trager	\(\frac {2 x^{\frac {7}{2}}}{7}\)	\(6\)
risch	\(\frac {2 x^{\frac {7}{2}}}{7}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/7*x^(7/2)

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Maxima [A]
time = 0.24, size = 5, normalized size = 0.56 \begin {gather*} \frac {2}{7} \, x^{\frac {7}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/7*x^(7/2)

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Fricas [A]
time = 0.59, size = 5, normalized size = 0.56 \begin {gather*} \frac {2}{7} \, x^{\frac {7}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/7*x^(7/2)

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Sympy [A]
time = 0.03, size = 7, normalized size = 0.78 \begin {gather*} \frac {2 x^{\frac {7}{2}}}{7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x**(7/2)/7

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Giac [A]
time = 0.00, size = 12, normalized size = 1.33 \begin {gather*} \frac {2}{7} \sqrt {x} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(5/2),x)

[Out]

2/7*x^(7/2)

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Mupad [B]
time = 0.08, size = 5, normalized size = 0.56 \begin {gather*} \frac {2\,x^{7/2}}{7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2*x^(7/2))/7

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