3.338 \(\int \frac{1}{\sqrt{a+b x}} \, dx\)

Optimal. Leaf size=14 \[ \frac{2 \sqrt{a+b x}}{b} \]

[Out]

(2*Sqrt[a + b*x])/b

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Rubi [A]  time = 0.00693339, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{2 \sqrt{a+b x}}{b} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[a + b*x],x]

[Out]

(2*Sqrt[a + b*x])/b

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Rubi in Sympy [A]  time = 1.27376, size = 10, normalized size = 0.71 \[ \frac{2 \sqrt{a + b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(a + b*x)/b

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Mathematica [A]  time = 0.00267762, size = 14, normalized size = 1. \[ \frac{2 \sqrt{a+b x}}{b} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[a + b*x],x]

[Out]

(2*Sqrt[a + b*x])/b

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Maple [A]  time = 0.005, size = 13, normalized size = 0.9 \[ 2\,{\frac{\sqrt{bx+a}}{b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x+a)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.34534, size = 16, normalized size = 1.14 \[ \frac{2 \, \sqrt{b x + a}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(b*x + a)/b

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Fricas [A]  time = 0.230638, size = 16, normalized size = 1.14 \[ \frac{2 \, \sqrt{b x + a}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(b*x + a)/b

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Sympy [A]  time = 0.038876, size = 10, normalized size = 0.71 \[ \frac{2 \sqrt{a + b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x+a)**(1/2),x)

[Out]

2*sqrt(a + b*x)/b

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GIAC/XCAS [A]  time = 0.21186, size = 16, normalized size = 1.14 \[ \frac{2 \, \sqrt{b x + a}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(b*x + a)/b