Optimal. Leaf size=10 \[ \log \left (a x+b x^2\right ) \]
[Out]
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Rubi [A] time = 0.0104052, 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 \[ \log \left (a x+b x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(a + 2*b*x)/(a*x + b*x^2),x]
[Out]
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Rubi in Sympy [A] time = 3.2558, size = 8, normalized size = 0.8 \[ \log{\left (a x + b x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*b*x+a)/(b*x**2+a*x),x)
[Out]
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Mathematica [A] time = 0.0063123, size = 9, normalized size = 0.9 \[ \log (a+b x)+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + 2*b*x)/(a*x + b*x^2),x]
[Out]
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Maple [A] time = 0., size = 9, normalized size = 0.9 \[ \ln \left ( x \left ( bx+a \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*b*x+a)/(b*x^2+a*x),x)
[Out]
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Maxima [A] time = 0.730641, size = 14, normalized size = 1.4 \[ \log \left (b x^{2} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*b*x + a)/(b*x^2 + a*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214917, size = 14, normalized size = 1.4 \[ \log \left (b x^{2} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*b*x + a)/(b*x^2 + a*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.07752, size = 8, normalized size = 0.8 \[ \log{\left (a x + b x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*b*x+a)/(b*x**2+a*x),x)
[Out]
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GIAC/XCAS [A] time = 0.206586, size = 15, normalized size = 1.5 \[{\rm ln}\left ({\left | b x + a \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*b*x + a)/(b*x^2 + a*x),x, algorithm="giac")
[Out]