Optimal. Leaf size=22 \[ (d-e) \log (x+1)-(d-2 e) \log (x+2) \]
[Out]
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Rubi [A] time = 0.0504856, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.115 \[ (d-e) \log (x+1)-(d-2 e) \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(2 - 3*x + x^2))/(4 - 5*x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 8.67422, size = 17, normalized size = 0.77 \[ - \left (d - 2 e\right ) \log{\left (x + 2 \right )} + \left (d - e\right ) \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2-3*x+2)/(x**4-5*x**2+4),x)
[Out]
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Mathematica [A] time = 0.0133759, size = 23, normalized size = 1.05 \[ (d-e) \log (x+1)+(2 e-d) \log (x+2) \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(2 - 3*x + x^2))/(4 - 5*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.008, size = 29, normalized size = 1.3 \[ -\ln \left ( 2+x \right ) d+2\,\ln \left ( 2+x \right ) e+\ln \left ( 1+x \right ) d-\ln \left ( 1+x \right ) e \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2-3*x+2)/(x^4-5*x^2+4),x)
[Out]
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Maxima [A] time = 0.703036, size = 30, normalized size = 1.36 \[ -{\left (d - 2 \, e\right )} \log \left (x + 2\right ) +{\left (d - e\right )} \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 - 3*x + 2)/(x^4 - 5*x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257359, size = 30, normalized size = 1.36 \[ -{\left (d - 2 \, e\right )} \log \left (x + 2\right ) +{\left (d - e\right )} \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 - 3*x + 2)/(x^4 - 5*x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.72595, size = 29, normalized size = 1.32 \[ \left (- d + 2 e\right ) \log{\left (x + \frac{4 d - 6 e}{2 d - 3 e} \right )} + \left (d - e\right ) \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2-3*x+2)/(x**4-5*x**2+4),x)
[Out]
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GIAC/XCAS [A] time = 0.283366, size = 35, normalized size = 1.59 \[ -{\left (d - 2 \, e\right )}{\rm ln}\left ({\left | x + 2 \right |}\right ) +{\left (d - e\right )}{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 - 3*x + 2)/(x^4 - 5*x^2 + 4),x, algorithm="giac")
[Out]