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

Optimal. Leaf size=19 \[ -\frac{2}{7 b x^2 \sqrt{b x^3}} \]

[Out]

-2/(7*b*x^2*Sqrt[b*x^3])

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Rubi [A]  time = 0.00827412, antiderivative size = 19, 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 \[ -\frac{2}{7 b x^2 \sqrt{b x^3}} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^3)^(-3/2),x]

[Out]

-2/(7*b*x^2*Sqrt[b*x^3])

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Rubi in Sympy [A]  time = 1.58104, size = 19, normalized size = 1. \[ - \frac{2 \sqrt{b x^{3}}}{7 b^{2} x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(b*x**3)/(7*b**2*x**5)

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Mathematica [A]  time = 0.00311791, size = 14, normalized size = 0.74 \[ -\frac{2 x}{7 \left (b x^3\right )^{3/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^3)^(-3/2),x]

[Out]

(-2*x)/(7*(b*x^3)^(3/2))

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Maple [A]  time = 0.002, size = 11, normalized size = 0.6 \[ -{\frac{2\,x}{7} \left ( b{x}^{3} \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x^3)^(3/2),x)

[Out]

-2/7*x/(b*x^3)^(3/2)

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Maxima [A]  time = 1.41801, size = 14, normalized size = 0.74 \[ -\frac{2 \, x}{7 \, \left (b x^{3}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/7*x/(b*x^3)^(3/2)

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Fricas [A]  time = 0.30623, size = 20, normalized size = 1.05 \[ -\frac{2 \, \sqrt{b x^{3}}}{7 \, b^{2} x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/7*sqrt(b*x^3)/(b^2*x^5)

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Sympy [A]  time = 1.87081, size = 17, normalized size = 0.89 \[ - \frac{2 x}{7 b^{\frac{3}{2}} \left (x^{3}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x**3)**(3/2),x)

[Out]

-2*x/(7*b**(3/2)*(x**3)**(3/2))

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GIAC/XCAS [A]  time = 0.589754, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sage0*x