Optimal. Leaf size=17 \[ \frac{1}{4} \log \left (x^4+2 x^2+4 x\right ) \]
[Out]
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Rubi [A] time = 0.00728313, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{1}{4} \log \left (x^4+2 x^2+4 x\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + x + x^3)/(4*x + 2*x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 6.53486, size = 12, normalized size = 0.71 \[ \frac{\log{\left (x \left (x^{3} + 2 x + 4\right ) \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3+x+1)/(x**4+2*x**2+4*x),x)
[Out]
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Mathematica [A] time = 0.00861106, size = 20, normalized size = 1.18 \[ \frac{1}{4} \log \left (x^3+2 x+4\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x + x^3)/(4*x + 2*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 0.8 \[{\frac{\ln \left ( x \left ({x}^{3}+2\,x+4 \right ) \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3+x+1)/(x^4+2*x^2+4*x),x)
[Out]
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Maxima [A] time = 1.32374, size = 20, normalized size = 1.18 \[ \frac{1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x + 1)/(x^4 + 2*x^2 + 4*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194932, size = 20, normalized size = 1.18 \[ \frac{1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x + 1)/(x^4 + 2*x^2 + 4*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.099663, size = 14, normalized size = 0.82 \[ \frac{\log{\left (x^{4} + 2 x^{2} + 4 x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3+x+1)/(x**4+2*x**2+4*x),x)
[Out]
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GIAC/XCAS [A] time = 0.219571, size = 24, normalized size = 1.41 \[ \frac{1}{4} \,{\rm ln}\left ({\left | x^{3} + 2 \, x + 4 \right |}\right ) + \frac{1}{4} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x + 1)/(x^4 + 2*x^2 + 4*x),x, algorithm="giac")
[Out]