Optimal. Leaf size=18 \[ -b \log (x)+b \log (1-b x)+\frac{1}{x} \]
[Out]
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Rubi [A] time = 0.0231498, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -b \log (x)+b \log (1-b x)+\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(-1 + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 3.78813, size = 15, normalized size = 0.83 \[ - b \log{\left (x \right )} + b \log{\left (- b x + 1 \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x-1),x)
[Out]
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Mathematica [A] time = 0.00434249, size = 18, normalized size = 1. \[ -b \log (x)+b \log (1-b x)+\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(-1 + b*x)),x]
[Out]
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Maple [A] time = 0.013, size = 18, normalized size = 1. \[{x}^{-1}-b\ln \left ( x \right ) +b\ln \left ( bx-1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x-1),x)
[Out]
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Maxima [A] time = 1.33982, size = 23, normalized size = 1.28 \[ b \log \left (b x - 1\right ) - b \log \left (x\right ) + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218869, size = 28, normalized size = 1.56 \[ \frac{b x \log \left (b x - 1\right ) - b x \log \left (x\right ) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.314871, size = 14, normalized size = 0.78 \[ b \left (- \log{\left (x \right )} + \log{\left (x - \frac{1}{b} \right )}\right ) + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x-1),x)
[Out]
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GIAC/XCAS [A] time = 0.207142, size = 26, normalized size = 1.44 \[ b{\rm ln}\left ({\left | b x - 1 \right |}\right ) - b{\rm ln}\left ({\left | x \right |}\right ) + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x^2),x, algorithm="giac")
[Out]