3.10 \(\int \frac{\sqrt{b x^2}}{x^5} \, dx\)

Optimal. Leaf size=16 \[ -\frac{\sqrt{b x^2}}{3 x^4} \]

[Out]

-Sqrt[b*x^2]/(3*x^4)

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Rubi [A]  time = 0.00668604, 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 \[ -\frac{\sqrt{b x^2}}{3 x^4} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^2]/x^5,x]

[Out]

-Sqrt[b*x^2]/(3*x^4)

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Rubi in Sympy [A]  time = 2.49698, size = 14, normalized size = 0.88 \[ - \frac{b^{2}}{3 \left (b x^{2}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(1/2)/x**5,x)

[Out]

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

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Mathematica [A]  time = 0.00206005, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{3 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^2]/x^5,x]

[Out]

-Sqrt[b*x^2]/(3*x^4)

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Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{3\,{x}^{4}}\sqrt{b{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(1/2)/x^5,x)

[Out]

-1/3*(b*x^2)^(1/2)/x^4

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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^5,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.254202, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^{2}}}{3 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^5,x, algorithm="fricas")

[Out]

-1/3*sqrt(b*x^2)/x^4

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Sympy [A]  time = 2.11264, size = 17, normalized size = 1.06 \[ - \frac{\sqrt{b} \sqrt{x^{2}}}{3 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(1/2)/x**5,x)

[Out]

-sqrt(b)*sqrt(x**2)/(3*x**4)

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GIAC/XCAS [A]  time = 0.22118, size = 14, normalized size = 0.88 \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x^5,x, algorithm="giac")

[Out]

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