Optimal. Leaf size=19 \[ \frac{x^3}{4 b \sqrt{\frac{b}{x^2}}} \]
[Out]
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Rubi [A] time = 0.00855059, 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 \[ \frac{x^3}{4 b \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Int[(b/x^2)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.55625, size = 15, normalized size = 0.79 \[ \frac{x^{5} \sqrt{\frac{b}{x^{2}}}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00366509, size = 14, normalized size = 0.74 \[ \frac{x}{4 \left (\frac{b}{x^2}\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x^2)^(-3/2),x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.6 \[{\frac{x}{4} \left ({\frac{b}{{x}^{2}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^2)^(3/2),x)
[Out]
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Maxima [A] time = 1.52109, size = 14, normalized size = 0.74 \[ \frac{x}{4 \, \left (\frac{b}{x^{2}}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222122, size = 20, normalized size = 1.05 \[ \frac{x^{5} \sqrt{\frac{b}{x^{2}}}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.88348, size = 15, normalized size = 0.79 \[ \frac{x}{4 b^{\frac{3}{2}} \left (\frac{1}{x^{2}}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**2)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.222346, size = 11, normalized size = 0.58 \[ \frac{x^{4}}{4 \, b^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-3/2),x, algorithm="giac")
[Out]