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