Optimal. Leaf size=10 \[ \log \left (b x+c x^2\right ) \]
[Out]
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Rubi [A] time = 0.00952077, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \log \left (b x+c x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x)/(b*x + c*x^2),x]
[Out]
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Rubi in Sympy [A] time = 3.22386, size = 8, normalized size = 0.8 \[ \log{\left (b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x+b)/(c*x**2+b*x),x)
[Out]
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Mathematica [A] time = 0.00619487, size = 9, normalized size = 0.9 \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x)/(b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 9, normalized size = 0.9 \[ \ln \left ( x \left ( cx+b \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x+b)/(c*x^2+b*x),x)
[Out]
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Maxima [A] time = 0.804943, size = 14, normalized size = 1.4 \[ \log \left (c x^{2} + b x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250039, size = 14, normalized size = 1.4 \[ \log \left (c x^{2} + b x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.0744, size = 8, normalized size = 0.8 \[ \log{\left (b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x+b)/(c*x**2+b*x),x)
[Out]
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GIAC/XCAS [A] time = 0.260005, size = 15, normalized size = 1.5 \[{\rm ln}\left ({\left | c x + b \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x),x, algorithm="giac")
[Out]