Optimal. Leaf size=14 \[ (d-2 e) \log (x+2)+e x \]
[Out]
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Rubi [A] time = 0.0397892, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065 \[ (d-2 e) \log (x+2)+e x \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \left (d - 2 e\right ) \log{\left (x + 2 \right )} + \int e\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**3-2*x**2-x+2)/(x**4-5*x**2+4),x)
[Out]
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Mathematica [A] time = 0.00731641, size = 16, normalized size = 1.14 \[ (d-2 e) \log (x+2)+e (x+2) \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.003, size = 18, normalized size = 1.3 \[ ex+\ln \left ( 2+x \right ) d-2\,\ln \left ( 2+x \right ) e \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^3-2*x^2-x+2)/(x^4-5*x^2+4),x)
[Out]
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Maxima [A] time = 0.708374, size = 19, normalized size = 1.36 \[ e x +{\left (d - 2 \, e\right )} \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 2*x^2 - x + 2)*(e*x + d)/(x^4 - 5*x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264118, size = 19, normalized size = 1.36 \[ e x +{\left (d - 2 \, e\right )} \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 2*x^2 - x + 2)*(e*x + d)/(x^4 - 5*x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.026, size = 12, normalized size = 0.86 \[ e x + \left (d - 2 e\right ) \log{\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**3-2*x**2-x+2)/(x**4-5*x**2+4),x)
[Out]
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GIAC/XCAS [A] time = 0.280264, size = 23, normalized size = 1.64 \[ x e +{\left (d - 2 \, e\right )}{\rm ln}\left ({\left | x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 2*x^2 - x + 2)*(e*x + d)/(x^4 - 5*x^2 + 4),x, algorithm="giac")
[Out]