3.23 \(\int \frac{1}{\sqrt{x}} \, dx\)

Optimal. Leaf size=7 \[ 2 \sqrt{x} \]

[Out]

2*Sqrt[x]

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Rubi [A]  time = 0.0004059, antiderivative size = 7, 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} \[ 2 \sqrt{x} \]

Antiderivative was successfully verified.

[In]

Int[1/Sqrt[x],x]

[Out]

2*Sqrt[x]

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}{\sqrt{x}} \, dx &=2 \sqrt{x}\\ \end{align*}

Mathematica [A]  time = 0.0006325, size = 7, normalized size = 1. \[ 2 \sqrt{x} \]

Antiderivative was successfully verified.

[In]

Integrate[1/Sqrt[x],x]

[Out]

2*Sqrt[x]

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Maple [A]  time = 0.002, size = 6, normalized size = 0.9 \begin{align*} 2\,\sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x^(1/2)

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Maxima [A]  time = 1.05939, size = 7, normalized size = 1. \begin{align*} 2 \, \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(x)

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Fricas [A]  time = 1.51773, size = 15, normalized size = 2.14 \begin{align*} 2 \, \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(x)

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Sympy [A]  time = 0.051554, size = 5, normalized size = 0.71 \begin{align*} 2 \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(x)

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Giac [A]  time = 1.11068, size = 7, normalized size = 1. \begin{align*} 2 \, \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(x)