3.37 \(\int \frac{1}{x \sqrt{b x^2}} \, dx\)

Optimal. Leaf size=11 \[ -\frac{1}{\sqrt{b x^2}} \]

[Out]

-(1/Sqrt[b*x^2])

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Rubi [A]  time = 0.00628959, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{1}{\sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[1/(x*Sqrt[b*x^2]),x]

[Out]

-(1/Sqrt[b*x^2])

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Rubi in Sympy [A]  time = 2.33053, size = 10, normalized size = 0.91 \[ - \frac{1}{\sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/sqrt(b*x**2)

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Mathematica [A]  time = 0.00367085, size = 15, normalized size = 1.36 \[ -\frac{b x^2}{\left (b x^2\right )^{3/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x*Sqrt[b*x^2]),x]

[Out]

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

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Maple [A]  time = 0.003, size = 10, normalized size = 0.9 \[ -{\frac{1}{\sqrt{b{x}^{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x/(b*x^2)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.44515, size = 11, normalized size = 1. \[ -\frac{1}{\sqrt{b} x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x),x, algorithm="maxima")

[Out]

-1/(sqrt(b)*x)

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Fricas [A]  time = 0.232776, size = 20, normalized size = 1.82 \[ -\frac{\sqrt{b x^{2}}}{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x),x, algorithm="fricas")

[Out]

-sqrt(b*x^2)/(b*x^2)

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Sympy [A]  time = 1.75118, size = 14, normalized size = 1.27 \[ - \frac{1}{\sqrt{b} \sqrt{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(sqrt(b)*sqrt(x**2))

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GIAC/XCAS [A]  time = 0.218588, size = 12, normalized size = 1.09 \[ -\frac{1}{\sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x),x, algorithm="giac")

[Out]

-1/sqrt(b*x^2)