Optimal. Leaf size=19 \[ -\frac{1}{2 b x \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00802965, 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 \[ -\frac{1}{2 b x \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.56596, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{2 b^{2} x^{3}} \]
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 = 0.00151832, size = 14, normalized size = 0.74 \[ -\frac{x}{2 \left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2)^(-3/2),x]
[Out]
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Maple [A] time = 0., size = 11, normalized size = 0.6 \[ -{\frac{x}{2} \left ( b{x}^{2} \right ) ^{-{\frac{3}{2}}}} \]
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 = 1.44336, size = 11, normalized size = 0.58 \[ -\frac{1}{2 \, b^{\frac{3}{2}} x^{2}} \]
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 = 0.229916, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{2 \, b^{2} x^{3}} \]
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 = 2.01922, size = 15, normalized size = 0.79 \[ - \frac{x}{2 b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}} \]
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 = 0.55815, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(-3/2),x, algorithm="giac")
[Out]