Optimal. Leaf size=11 \[ -\frac{1}{\sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00628959, antiderivative size = 11, 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 \[ -\frac{1}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[b*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 2.33053, size = 10, normalized size = 0.91 \[ - \frac{1}{\sqrt{b x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00367085, size = 15, normalized size = 1.36 \[ -\frac{b x^2}{\left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[b*x^2]),x]
[Out]
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Maple [A] time = 0.003, size = 10, normalized size = 0.9 \[ -{\frac{1}{\sqrt{b{x}^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.44515, size = 11, normalized size = 1. \[ -\frac{1}{\sqrt{b} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232776, size = 20, normalized size = 1.82 \[ -\frac{\sqrt{b x^{2}}}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.75118, size = 14, normalized size = 1.27 \[ - \frac{1}{\sqrt{b} \sqrt{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.218588, size = 12, normalized size = 1.09 \[ -\frac{1}{\sqrt{b x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x),x, algorithm="giac")
[Out]