Optimal. Leaf size=18 \[ \frac{1}{2} \log \left (1-b x^2\right )-\log (x) \]
[Out]
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Rubi [A] time = 0.0313369, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{1}{2} \log \left (1-b x^2\right )-\log (x) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(-1 + b*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 5.16496, size = 15, normalized size = 0.83 \[ - \frac{\log{\left (x^{2} \right )}}{2} + \frac{\log{\left (- b x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**2-1),x)
[Out]
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Mathematica [A] time = 0.00802293, size = 18, normalized size = 1. \[ \frac{1}{2} \log \left (1-b x^2\right )-\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(-1 + b*x^2)),x]
[Out]
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \[ -\ln \left ( x \right ) +{\frac{\ln \left ( b{x}^{2}-1 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^2-1),x)
[Out]
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Maxima [A] time = 1.33542, size = 23, normalized size = 1.28 \[ \frac{1}{2} \, \log \left (b x^{2} - 1\right ) - \frac{1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 - 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227538, size = 20, normalized size = 1.11 \[ \frac{1}{2} \, \log \left (b x^{2} - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 - 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.308755, size = 12, normalized size = 0.67 \[ - \log{\left (x \right )} + \frac{\log{\left (x^{2} - \frac{1}{b} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**2-1),x)
[Out]
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GIAC/XCAS [A] time = 0.219233, size = 24, normalized size = 1.33 \[ -\frac{1}{2} \,{\rm ln}\left (x^{2}\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | b x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 - 1)*x),x, algorithm="giac")
[Out]