3.22 \(\int \sqrt{x} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.000424, 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} \[ \frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]

Int[Sqrt[x],x]

[Out]

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

Mathematica [A]  time = 0.0008817, size = 9, normalized size = 1. \[ \frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]

Integrate[Sqrt[x],x]

[Out]

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

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Maple [A]  time = 0., 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(x^(1/2),x)

[Out]

2/3*x^(3/2)

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Maxima [A]  time = 1.03761, 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(x^(1/2),x, algorithm="maxima")

[Out]

2/3*x^(3/2)

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Fricas [A]  time = 1.55057, size = 18, normalized size = 2. \begin{align*} \frac{2}{3} \, x^{\frac{3}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/3*x^(3/2)

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Sympy [A]  time = 0.051497, size = 7, normalized size = 0.78 \begin{align*} \frac{2 x^{\frac{3}{2}}}{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 1.12254, 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(x^(1/2),x, algorithm="giac")

[Out]

2/3*x^(3/2)