Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^2\right )}{2 b} \]
[Out]
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Rubi [A] time = 0.0152597, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\log \left (a+b x^2\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a*x + b*x^3),x]
[Out]
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Rubi in Sympy [A] time = 3.3114, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{2} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x**3+a*x),x)
[Out]
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Mathematica [A] time = 0.0029752, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^2\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a*x + b*x^3),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{2}+a \right ) }{2\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x^3+a*x),x)
[Out]
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Maxima [A] time = 1.40561, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{2} + a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200772, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{2} + a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.244588, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{2} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x**3+a*x),x)
[Out]
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GIAC/XCAS [A] time = 0.215477, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{2} + a \right |}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x),x, algorithm="giac")
[Out]