Optimal. Leaf size=18 \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
[Out]
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Rubi [A] time = 0.0195302, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.364 \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
Antiderivative was successfully verified.
[In] Int[(b*x + c*x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 4.09515, size = 12, normalized size = 0.67 \[ \frac{\log{\left (x \right )}}{b} - \frac{\log{\left (b + c x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(c*x**2+b*x),x)
[Out]
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Mathematica [A] time = 0.0051994, size = 18, normalized size = 1. \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x + c*x^2)^(-1),x]
[Out]
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Maple [A] time = 0.008, size = 19, normalized size = 1.1 \[{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( cx+b \right ) }{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(c*x^2+b*x),x)
[Out]
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Maxima [A] time = 0.699161, size = 24, normalized size = 1.33 \[ -\frac{\log \left (c x + b\right )}{b} + \frac{\log \left (x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(c*x^2 + b*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22265, size = 22, normalized size = 1.22 \[ -\frac{\log \left (c x + b\right ) - \log \left (x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(c*x^2 + b*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.329503, size = 10, normalized size = 0.56 \[ \frac{\log{\left (x \right )} - \log{\left (\frac{b}{c} + x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(c*x**2+b*x),x)
[Out]
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GIAC/XCAS [A] time = 0.205105, size = 27, normalized size = 1.5 \[ -\frac{{\rm ln}\left ({\left | c x + b \right |}\right )}{b} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(c*x^2 + b*x),x, algorithm="giac")
[Out]