Optimal. Leaf size=29 \[ \frac{x^3}{3}-2 x^2+12 x-\frac{16}{x+2}-32 \log (x+2) \]
[Out]
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Rubi [A] time = 0.0362909, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{x^3}{3}-2 x^2+12 x-\frac{16}{x+2}-32 \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[x^4/(4 + 4*x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{3}}{3} + 12 x - 32 \log{\left (x + 2 \right )} - 4 \int x\, dx - \frac{16}{x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(x**2+4*x+4),x)
[Out]
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Mathematica [A] time = 0.0177923, size = 30, normalized size = 1.03 \[ \frac{1}{3} \left (x^3-6 x^2+36 x-\frac{48}{x+2}-96 \log (x+2)+104\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(4 + 4*x + x^2),x]
[Out]
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Maple [A] time = 0.009, size = 28, normalized size = 1. \[ 12\,x-2\,{x}^{2}+{\frac{{x}^{3}}{3}}-16\, \left ( 2+x \right ) ^{-1}-32\,\ln \left ( 2+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(x^2+4*x+4),x)
[Out]
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Maxima [A] time = 0.681258, size = 36, normalized size = 1.24 \[ \frac{1}{3} \, x^{3} - 2 \, x^{2} + 12 \, x - \frac{16}{x + 2} - 32 \, \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^2 + 4*x + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199066, size = 46, normalized size = 1.59 \[ \frac{x^{4} - 4 \, x^{3} + 24 \, x^{2} - 96 \,{\left (x + 2\right )} \log \left (x + 2\right ) + 72 \, x - 48}{3 \,{\left (x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^2 + 4*x + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.148384, size = 24, normalized size = 0.83 \[ \frac{x^{3}}{3} - 2 x^{2} + 12 x - 32 \log{\left (x + 2 \right )} - \frac{16}{x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(x**2+4*x+4),x)
[Out]
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GIAC/XCAS [A] time = 0.204577, size = 38, normalized size = 1.31 \[ \frac{1}{3} \, x^{3} - 2 \, x^{2} + 12 \, x - \frac{16}{x + 2} - 32 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^2 + 4*x + 4),x, algorithm="giac")
[Out]