3.86 \(\int \left (\frac{b}{x}\right )^{3/2} \, dx\)

Optimal. Leaf size=12 \[ -2 b \sqrt{\frac{b}{x}} \]

[Out]

-2*b*Sqrt[b/x]

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Rubi [A]  time = 0.00738873, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -2 b \sqrt{\frac{b}{x}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x)^(3/2),x]

[Out]

-2*b*Sqrt[b/x]

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Rubi in Sympy [A]  time = 1.27488, size = 10, normalized size = 0.83 \[ - 2 b \sqrt{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x)**(3/2),x)

[Out]

-2*b*sqrt(b/x)

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Mathematica [A]  time = 0.00243123, size = 12, normalized size = 1. \[ -2 x \left (\frac{b}{x}\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x)^(3/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ -2\,x \left ({\frac{b}{x}} \right ) ^{3/2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x)^(3/2),x)

[Out]

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

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Maxima [A]  time = 1.44042, size = 14, normalized size = 1.17 \[ -2 \, x \left (\frac{b}{x}\right )^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.244867, size = 14, normalized size = 1.17 \[ -2 \, b \sqrt{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*b*sqrt(b/x)

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Sympy [A]  time = 1.08561, size = 15, normalized size = 1.25 \[ - 2 b^{\frac{3}{2}} x \left (\frac{1}{x}\right )^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x)**(3/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.227414, size = 16, normalized size = 1.33 \[ -\frac{2 \, b^{2}{\rm sign}\left (x\right )}{\sqrt{b x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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