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 = 0.00701051, 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 \[ \frac{2 \sqrt{b x}}{b} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[b*x],x]

[Out]

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

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Rubi in Sympy [A]  time = 1.37099, size = 8, normalized size = 0.67 \[ \frac{2 \sqrt{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b*x)**(1/2),x)

[Out]

2*sqrt(b*x)/b

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Mathematica [A]  time = 0.00250163, 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 = 0.003, size = 9, normalized size = 0.8 \[ 2\,{\frac{x}{\sqrt{bx}}} \]

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 = 1.45594, size = 14, normalized size = 1.17 \[ \frac{2 \, \sqrt{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x),x, algorithm="maxima")

[Out]

2*sqrt(b*x)/b

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Fricas [A]  time = 0.2521, size = 14, normalized size = 1.17 \[ \frac{2 \, \sqrt{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x),x, algorithm="fricas")

[Out]

2*sqrt(b*x)/b

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Sympy [A]  time = 0.064073, size = 8, normalized size = 0.67 \[ \frac{2 \sqrt{b x}}{b} \]

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/XCAS [A]  time = 0.216261, size = 14, normalized size = 1.17 \[ \frac{2 \, \sqrt{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x),x, algorithm="giac")

[Out]

2*sqrt(b*x)/b