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

Optimal. Leaf size=12 \[ \frac{2 \sqrt{b x}}{b} \]

[Out]

(2*Sqrt[b*x])/b

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Rubi [A]  time = 0.0011501, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ \frac{2 \sqrt{b x}}{b} \]

Antiderivative was successfully verified.

[In]

Int[1/Sqrt[b*x],x]

[Out]

(2*Sqrt[b*x])/b

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

\begin{align*} \int \frac{1}{\sqrt{b x}} \, dx &=\frac{2 \sqrt{b x}}{b}\\ \end{align*}

Mathematica [A]  time = 0.0009336, size = 10, normalized size = 0.83 \[ \frac{2 x}{\sqrt{b x}} \]

Antiderivative was successfully verified.

[In]

Integrate[1/Sqrt[b*x],x]

[Out]

(2*x)/Sqrt[b*x]

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Maple [A]  time = 0.001, size = 9, normalized size = 0.8 \begin{align*} 2\,{\frac{x}{\sqrt{bx}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x/(b*x)^(1/2)

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Maxima [A]  time = 0.995181, size = 14, normalized size = 1.17 \begin{align*} \frac{2 \, \sqrt{b x}}{b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(b*x)/b

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Fricas [A]  time = 1.68011, size = 20, normalized size = 1.67 \begin{align*} \frac{2 \, \sqrt{b x}}{b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(b*x)/b

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Sympy [A]  time = 0.072576, size = 8, normalized size = 0.67 \begin{align*} \frac{2 \sqrt{b x}}{b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(b*x)/b

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Giac [A]  time = 1.14185, size = 14, normalized size = 1.17 \begin{align*} \frac{2 \, \sqrt{b x}}{b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*sqrt(b*x)/b