Optimal. Leaf size=19 \[ \frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}} \]
[Out]
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Rubi [A] time = 0.00925679, 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 \[ \frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
[In] Int[(b/x^3)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.59001, size = 17, normalized size = 0.89 \[ \frac{2 x^{7} \sqrt{\frac{b}{x^{3}}}}{11 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**3)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00371564, size = 14, normalized size = 0.74 \[ \frac{2 x}{11 \left (\frac{b}{x^3}\right )^{3/2}} \]
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 = 0.6 \[{\frac{2\,x}{11} \left ({\frac{b}{{x}^{3}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^3)^(3/2),x)
[Out]
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Maxima [A] time = 1.44128, size = 14, normalized size = 0.74 \[ \frac{2 \, x}{11 \, \left (\frac{b}{x^{3}}\right )^{\frac{3}{2}}} \]
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 = 0.221238, size = 20, normalized size = 1.05 \[ \frac{2 \, x^{7} \sqrt{\frac{b}{x^{3}}}}{11 \, b^{2}} \]
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 = 1.88407, size = 17, normalized size = 0.89 \[ \frac{2 x}{11 b^{\frac{3}{2}} \left (\frac{1}{x^{3}}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**3)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (\frac{b}{x^{3}}\right )^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^3)^(-3/2),x, algorithm="giac")
[Out]