3.20 \(\int x^{3/2} \, dx\)

Optimal. Leaf size=9 \[ \frac {2 x^{5/2}}{5} \]

[Out]

2/5*x^(5/2)

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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} \[ \frac {2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]

Int[x^(3/2),x]

[Out]

(2*x^(5/2))/5

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

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \[ \frac {2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(3/2),x]

[Out]

(2*x^(5/2))/5

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fricas [A]  time = 0.41, size = 5, normalized size = 0.56 \[ \frac {2}{5} \, x^{\frac {5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="fricas")

[Out]

2/5*x^(5/2)

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giac [A]  time = 0.95, size = 5, normalized size = 0.56 \[ \frac {2}{5} \, x^{\frac {5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="giac")

[Out]

2/5*x^(5/2)

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maple [A]  time = 0.00, size = 6, normalized size = 0.67 \[ \frac {2 x^{\frac {5}{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(3/2),x)

[Out]

2/5*x^(5/2)

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maxima [A]  time = 0.51, size = 5, normalized size = 0.56 \[ \frac {2}{5} \, x^{\frac {5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="maxima")

[Out]

2/5*x^(5/2)

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mupad [B]  time = 0.04, size = 5, normalized size = 0.56 \[ \frac {2\,x^{5/2}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(3/2),x)

[Out]

(2*x^(5/2))/5

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sympy [A]  time = 0.06, size = 7, normalized size = 0.78 \[ \frac {2 x^{\frac {5}{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**(3/2),x)

[Out]

2*x**(5/2)/5

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