Optimal. Leaf size=16 \[ -\frac{1}{2 x \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00664285, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{1}{2 x \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*Sqrt[b*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 2.49238, size = 15, normalized size = 0.94 \[ - \frac{\sqrt{b x^{2}}}{2 b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00420618, size = 15, normalized size = 0.94 \[ -\frac{b x}{2 \left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*Sqrt[b*x^2]),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \[ -{\frac{1}{2\,x}{\frac{1}{\sqrt{b{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.41343, size = 11, normalized size = 0.69 \[ -\frac{1}{2 \, \sqrt{b} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21336, size = 20, normalized size = 1.25 \[ -\frac{\sqrt{b x^{2}}}{2 \, b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.91366, size = 17, normalized size = 1.06 \[ - \frac{1}{2 \sqrt{b} x \sqrt{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.572773, size = 4, normalized size = 0.25 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^2),x, algorithm="giac")
[Out]