Optimal. Leaf size=15 \[ \log (x)-\frac{1}{2} \log \left (b x^2+1\right ) \]
[Out]
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Rubi [A] time = 0.0254655, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.556 \[ \log (x)-\frac{1}{2} \log \left (b x^2+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(x + b*x^3)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 25.0264, size = 15, normalized size = 1. \[ \frac{\log{\left (x^{2} \right )}}{2} - \frac{\log{\left (b x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**3+x),x)
[Out]
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Mathematica [A] time = 0.00553795, size = 15, normalized size = 1. \[ \log (x)-\frac{1}{2} \log \left (b x^2+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(x + b*x^3)^(-1),x]
[Out]
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Maple [A] time = 0.006, size = 14, normalized size = 0.9 \[ \ln \left ( x \right ) -{\frac{\ln \left ( b{x}^{2}+1 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^3+x),x)
[Out]
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Maxima [A] time = 1.37166, size = 18, normalized size = 1.2 \[ -\frac{1}{2} \, \log \left (b x^{2} + 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^3 + x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200676, size = 18, normalized size = 1.2 \[ -\frac{1}{2} \, \log \left (b x^{2} + 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^3 + x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.28776, size = 12, normalized size = 0.8 \[ \log{\left (x \right )} - \frac{\log{\left (x^{2} + \frac{1}{b} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.216922, size = 24, normalized size = 1.6 \[ \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | b x^{2} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^3 + x),x, algorithm="giac")
[Out]