Optimal. Leaf size=23 \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^2\right )}{2 a} \]
[Out]
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Rubi [A] time = 0.0367481, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^2\right )}{2 a} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a - b*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 6.48221, size = 19, normalized size = 0.83 \[ \frac{\log{\left (x^{2} \right )}}{2 a} - \frac{\log{\left (a - b x^{2} \right )}}{2 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(-b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.0110714, size = 23, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^2\right )}{2 a} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a - b*x^2)),x]
[Out]
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Maple [A] time = 0.006, size = 23, normalized size = 1. \[{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( b{x}^{2}-a \right ) }{2\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(-b*x^2+a),x)
[Out]
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Maxima [A] time = 1.35458, size = 34, normalized size = 1.48 \[ -\frac{\log \left (b x^{2} - a\right )}{2 \, a} + \frac{\log \left (x^{2}\right )}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210973, size = 27, normalized size = 1.17 \[ -\frac{\log \left (b x^{2} - a\right ) - 2 \, \log \left (x\right )}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.530493, size = 15, normalized size = 0.65 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (- \frac{a}{b} + x^{2} \right )}}{2 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(-b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.209211, size = 35, normalized size = 1.52 \[ \frac{{\rm ln}\left (x^{2}\right )}{2 \, a} - \frac{{\rm ln}\left ({\left | b x^{2} - a \right |}\right )}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x),x, algorithm="giac")
[Out]