Optimal. Leaf size=10 \[ \frac{1}{x^2+1}+\log (x) \]
[Out]
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Rubi [A] time = 0.0477536, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{x^2+1}+\log (x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^4)/(x*(1 + x^2)^2),x]
[Out]
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Rubi in Sympy [A] time = 3.57674, size = 12, normalized size = 1.2 \[ \frac{\log{\left (x^{2} \right )}}{2} + \frac{1}{x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**4+1)/x/(x**2+1)**2,x)
[Out]
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Mathematica [A] time = 0.00844627, size = 10, normalized size = 1. \[ \frac{1}{x^2+1}+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^4)/(x*(1 + x^2)^2),x]
[Out]
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Maple [A] time = 0., size = 11, normalized size = 1.1 \[ \left ({x}^{2}+1 \right ) ^{-1}+\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^4+1)/x/(x^2+1)^2,x)
[Out]
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Maxima [A] time = 1.38651, size = 19, normalized size = 1.9 \[ \frac{1}{x^{2} + 1} + \frac{1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 1)/((x^2 + 1)^2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193307, size = 24, normalized size = 2.4 \[ \frac{{\left (x^{2} + 1\right )} \log \left (x\right ) + 1}{x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 1)/((x^2 + 1)^2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.104472, size = 8, normalized size = 0.8 \[ \log{\left (x \right )} + \frac{1}{x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**4+1)/x/(x**2+1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211513, size = 19, normalized size = 1.9 \[ \frac{1}{x^{2} + 1} + \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 1)/((x^2 + 1)^2*x),x, algorithm="giac")
[Out]