Optimal. Leaf size=21 \[ \frac{1}{6} \log \left (x^2+1\right )-\frac{1}{6} \log \left (x^2+4\right ) \]
[Out]
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Rubi [A] time = 0.0377833, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{1}{6} \log \left (x^2+1\right )-\frac{1}{6} \log \left (x^2+4\right ) \]
Antiderivative was successfully verified.
[In] Int[x/((1 + x^2)*(4 + x^2)),x]
[Out]
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Rubi in Sympy [A] time = 6.70731, size = 15, normalized size = 0.71 \[ \frac{\log{\left (x^{2} + 1 \right )}}{6} - \frac{\log{\left (x^{2} + 4 \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**2+1)/(x**2+4),x)
[Out]
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Mathematica [A] time = 0.00697595, size = 21, normalized size = 1. \[ \frac{1}{6} \log \left (x^2+1\right )-\frac{1}{6} \log \left (x^2+4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/((1 + x^2)*(4 + x^2)),x]
[Out]
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Maple [A] time = 0.009, size = 18, normalized size = 0.9 \[{\frac{\ln \left ({x}^{2}+1 \right ) }{6}}-{\frac{\ln \left ({x}^{2}+4 \right ) }{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^2+1)/(x^2+4),x)
[Out]
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Maxima [A] time = 1.33336, size = 23, normalized size = 1.1 \[ -\frac{1}{6} \, \log \left (x^{2} + 4\right ) + \frac{1}{6} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x^2 + 4)*(x^2 + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222726, size = 23, normalized size = 1.1 \[ -\frac{1}{6} \, \log \left (x^{2} + 4\right ) + \frac{1}{6} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x^2 + 4)*(x^2 + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.205388, size = 15, normalized size = 0.71 \[ \frac{\log{\left (x^{2} + 1 \right )}}{6} - \frac{\log{\left (x^{2} + 4 \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**2+1)/(x**2+4),x)
[Out]
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GIAC/XCAS [A] time = 0.23364, size = 23, normalized size = 1.1 \[ -\frac{1}{6} \,{\rm ln}\left (x^{2} + 4\right ) + \frac{1}{6} \,{\rm ln}\left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x^2 + 4)*(x^2 + 1)),x, algorithm="giac")
[Out]