Optimal. Leaf size=10 \[ \log \left (a x+b x^3\right ) \]
[Out]
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Rubi [A] time = 0.0103937, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \log \left (a x+b x^3\right ) \]
Antiderivative was successfully verified.
[In] Int[(a + 3*b*x^2)/(a*x + b*x^3),x]
[Out]
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Rubi in Sympy [A] time = 12.4693, size = 14, normalized size = 1.4 \[ \frac{\log{\left (x^{2} \right )}}{2} + \log{\left (a + b x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*b*x**2+a)/(b*x**3+a*x),x)
[Out]
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Mathematica [A] time = 0.00922223, size = 11, normalized size = 1.1 \[ \log \left (a+b x^2\right )+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + 3*b*x^2)/(a*x + b*x^3),x]
[Out]
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Maple [A] time = 0.002, size = 11, normalized size = 1.1 \[ \ln \left ( x \left ( b{x}^{2}+a \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*b*x^2+a)/(b*x^3+a*x),x)
[Out]
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Maxima [A] time = 0.789497, size = 14, normalized size = 1.4 \[ \log \left (b x^{3} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*b*x^2 + a)/(b*x^3 + a*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259774, size = 14, normalized size = 1.4 \[ \log \left (b x^{3} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*b*x^2 + a)/(b*x^3 + a*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.11232, size = 8, normalized size = 0.8 \[ \log{\left (a x + b x^{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*b*x**2+a)/(b*x**3+a*x),x)
[Out]
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GIAC/XCAS [A] time = 0.261366, size = 22, normalized size = 2.2 \[ \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) +{\rm ln}\left ({\left | b x^{2} + a \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*b*x^2 + a)/(b*x^3 + a*x),x, algorithm="giac")
[Out]