Optimal. Leaf size=17 \[ -\frac{1}{2} \log \left (x^2+1\right )+4 \log (x)+\tan ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.0560719, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.312 \[ -\frac{1}{2} \log \left (x^2+1\right )+4 \log (x)+\tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[(4 + x + 3*x^2)/(x + x^3),x]
[Out]
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Rubi in Sympy [A] time = 8.40866, size = 15, normalized size = 0.88 \[ 4 \log{\left (x \right )} - \frac{\log{\left (x^{2} + 1 \right )}}{2} + \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*x**2+x+4)/(x**3+x),x)
[Out]
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Mathematica [A] time = 0.00711386, size = 17, normalized size = 1. \[ -\frac{1}{2} \log \left (x^2+1\right )+4 \log (x)+\tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[(4 + x + 3*x^2)/(x + x^3),x]
[Out]
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Maple [A] time = 0.007, size = 16, normalized size = 0.9 \[ \arctan \left ( x \right ) +4\,\ln \left ( x \right ) -{\frac{\ln \left ({x}^{2}+1 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*x^2+x+4)/(x^3+x),x)
[Out]
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Maxima [A] time = 0.891133, size = 20, normalized size = 1.18 \[ \arctan \left (x\right ) - \frac{1}{2} \, \log \left (x^{2} + 1\right ) + 4 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + x + 4)/(x^3 + x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25447, size = 20, normalized size = 1.18 \[ \arctan \left (x\right ) - \frac{1}{2} \, \log \left (x^{2} + 1\right ) + 4 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + x + 4)/(x^3 + x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.294637, size = 15, normalized size = 0.88 \[ 4 \log{\left (x \right )} - \frac{\log{\left (x^{2} + 1 \right )}}{2} + \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x**2+x+4)/(x**3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.259018, size = 22, normalized size = 1.29 \[ \arctan \left (x\right ) - \frac{1}{2} \,{\rm ln}\left (x^{2} + 1\right ) + 4 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + x + 4)/(x^3 + x),x, algorithm="giac")
[Out]