3.97 \(\int \frac{1}{(b x)^{3/2}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00656573, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{2}{b \sqrt{b x}} \]

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 = 1.33349, size = 10, normalized size = 0.83 \[ - \frac{2}{b \sqrt{b x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00202389, size = 10, normalized size = 0.83 \[ -\frac{2 x}{(b x)^{3/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(-3/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 9, normalized size = 0.8 \[ -2\,{\frac{x}{ \left ( bx \right ) ^{3/2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x)^(3/2),x)

[Out]

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

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Maxima [A]  time = 1.42175, size = 14, normalized size = 1.17 \[ -\frac{2}{\sqrt{b x} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.216931, size = 14, normalized size = 1.17 \[ -\frac{2}{\sqrt{b x} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.070462, size = 10, normalized size = 0.83 \[ - \frac{2}{b \sqrt{b x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x)**(3/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.227453, size = 14, normalized size = 1.17 \[ -\frac{2}{\sqrt{b x} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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