3.8 \(\int \frac{\sqrt{b x^2}}{x^3} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00675452, antiderivative size = 14, 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 \[ -\frac{\sqrt{b x^2}}{x^2} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^2]/x^3,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.43338, size = 10, normalized size = 0.71 \[ - \frac{b}{\sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(1/2)/x**3,x)

[Out]

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

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Mathematica [A]  time = 0.00349005, size = 14, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^2]/x^3,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.9 \[ -{\frac{1}{{x}^{2}}\sqrt{b{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(1/2)/x^3,x)

[Out]

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

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^3,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.247893, size = 16, normalized size = 1.14 \[ -\frac{\sqrt{b x^{2}}}{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^3,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 1.60944, size = 15, normalized size = 1.07 \[ - \frac{\sqrt{b} \sqrt{x^{2}}}{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(1/2)/x**3,x)

[Out]

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

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GIAC/XCAS [A]  time = 0.212573, size = 14, normalized size = 1. \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^3,x, algorithm="giac")

[Out]

-sqrt(b)*sign(x)/x