Optimal. Leaf size=11 \[ \log (x)+\frac{1}{2} \tan ^{-1}(2 x) \]
[Out]
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Rubi [A] time = 0.0482499, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \log (x)+\frac{1}{2} \tan ^{-1}(2 x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x + 4*x^2)/(x + 4*x^3),x]
[Out]
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Rubi in Sympy [A] time = 7.83613, size = 8, normalized size = 0.73 \[ \log{\left (x \right )} + \frac{\operatorname{atan}{\left (2 x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**2+x+1)/(4*x**3+x),x)
[Out]
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Mathematica [A] time = 0.00733817, size = 11, normalized size = 1. \[ \log (x)+\frac{1}{2} \tan ^{-1}(2 x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x + 4*x^2)/(x + 4*x^3),x]
[Out]
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Maple [A] time = 0.007, size = 10, normalized size = 0.9 \[{\frac{\arctan \left ( 2\,x \right ) }{2}}+\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^2+x+1)/(4*x^3+x),x)
[Out]
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Maxima [A] time = 0.877128, size = 12, normalized size = 1.09 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + x + 1)/(4*x^3 + x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.290213, size = 12, normalized size = 1.09 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + x + 1)/(4*x^3 + x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.39055, size = 8, normalized size = 0.73 \[ \log{\left (x \right )} + \frac{\operatorname{atan}{\left (2 x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**2+x+1)/(4*x**3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.263086, size = 14, normalized size = 1.27 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + x + 1)/(4*x^3 + x),x, algorithm="giac")
[Out]