3.9 \(\int \frac{\sqrt{b x^2}}{x^4} \, dx\)

Optimal. Leaf size=16 \[ -\frac{\sqrt{b x^2}}{2 x^3} \]

[Out]

-Sqrt[b*x^2]/(2*x^3)

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Rubi [A]  time = 0.00678716, antiderivative size = 16, 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 \[ -\frac{\sqrt{b x^2}}{2 x^3} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^2]/x^4,x]

[Out]

-Sqrt[b*x^2]/(2*x^3)

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Rubi in Sympy [A]  time = 1.92961, size = 14, normalized size = 0.88 \[ - \frac{\sqrt{b x^{2}}}{2 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(1/2)/x**4,x)

[Out]

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

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Mathematica [A]  time = 0.00207829, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{2 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^2]/x^4,x]

[Out]

-Sqrt[b*x^2]/(2*x^3)

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Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{2\,{x}^{3}}\sqrt{b{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(1/2)/x^4,x)

[Out]

-1/2*(b*x^2)^(1/2)/x^3

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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^4,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.253553, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^{2}}}{2 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^4,x, algorithm="fricas")

[Out]

-1/2*sqrt(b*x^2)/x^3

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Sympy [A]  time = 1.90889, size = 17, normalized size = 1.06 \[ - \frac{\sqrt{b} \sqrt{x^{2}}}{2 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(1/2)/x**4,x)

[Out]

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

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GIAC/XCAS [A]  time = 0.214985, size = 14, normalized size = 0.88 \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^4,x, algorithm="giac")

[Out]

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