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

Optimal. Leaf size=17 \[ -\frac{2 b \sqrt{\frac{b}{x^3}}}{7 x^2} \]

[Out]

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

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Rubi [A]  time = 0.00794486, antiderivative size = 17, 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 \[ -\frac{2 b \sqrt{\frac{b}{x^3}}}{7 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^3)^(3/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.33267, size = 17, normalized size = 1. \[ - \frac{2 b \sqrt{\frac{b}{x^{3}}}}{7 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.0023298, size = 14, normalized size = 0.82 \[ -\frac{2}{7} x \left (\frac{b}{x^3}\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^3)^(3/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.7 \[ -{\frac{2\,x}{7} \left ({\frac{b}{{x}^{3}}} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^3)^(3/2),x)

[Out]

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

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Maxima [A]  time = 1.43417, size = 14, normalized size = 0.82 \[ -\frac{2}{7} \, x \left (\frac{b}{x^{3}}\right )^{\frac{3}{2}} \]

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 = 0.251366, size = 18, normalized size = 1.06 \[ -\frac{2 \, b \sqrt{\frac{b}{x^{3}}}}{7 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.9308, size = 19, normalized size = 1.12 \[ - \frac{2 b^{\frac{3}{2}} x \left (\frac{1}{x^{3}}\right )^{\frac{3}{2}}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**3)**(3/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.225932, size = 18, normalized size = 1.06 \[ -\frac{2 \, b^{2}}{7 \, \sqrt{b x} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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