Optimal. Leaf size=14 \[ -\frac{1}{b \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00728729, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{1}{b \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[x/(b*x^2)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.1282, size = 12, normalized size = 0.86 \[ - \frac{1}{b \sqrt{b x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00166711, size = 14, normalized size = 1. \[ -\frac{x^2}{\left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(b*x^2)^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 13, normalized size = 0.9 \[ -{{x}^{2} \left ( b{x}^{2} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^2)^(3/2),x)
[Out]
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Maxima [A] time = 1.42954, size = 16, normalized size = 1.14 \[ -\frac{1}{\sqrt{b x^{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216547, size = 20, normalized size = 1.43 \[ -\frac{\sqrt{b x^{2}}}{b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.96215, size = 15, normalized size = 1.07 \[ - \frac{x^{2}}{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x**2)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209495, size = 16, normalized size = 1.14 \[ -\frac{1}{\sqrt{b x^{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(3/2),x, algorithm="giac")
[Out]