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