Optimal. Leaf size=28 \[ \frac{6}{x+1}-\frac{6}{(x+1)^2}+\frac{8}{3 (x+1)^3}+\log (x+1) \]
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Rubi [A] time = 0.0508693, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 34, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{6}{x+1}-\frac{6}{(x+1)^2}+\frac{8}{3 (x+1)^3}+\log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(-1 + 3*x - 3*x^2 + x^3)/(1 + 4*x + 6*x^2 + 4*x^3 + x^4),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int ^{x + 1} \frac{x^{3} - 6 x^{2} + 12 x - 8}{x^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-3*x**2+3*x-1)/(x**4+4*x**3+6*x**2+4*x+1),x)
[Out]
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Mathematica [A] time = 0.0197026, size = 24, normalized size = 0.86 \[ \frac{2 \left (9 x^2+9 x+4\right )}{3 (x+1)^3}+\log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + 3*x - 3*x^2 + x^3)/(1 + 4*x + 6*x^2 + 4*x^3 + x^4),x]
[Out]
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Maple [A] time = 0.01, size = 27, normalized size = 1. \[{\frac{8}{3\, \left ( 1+x \right ) ^{3}}}-6\, \left ( 1+x \right ) ^{-2}+6\, \left ( 1+x \right ) ^{-1}+\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-3*x^2+3*x-1)/(x^4+4*x^3+6*x^2+4*x+1),x)
[Out]
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Maxima [A] time = 0.830648, size = 43, normalized size = 1.54 \[ \frac{2 \,{\left (9 \, x^{2} + 9 \, x + 4\right )}}{3 \,{\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )}} + \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/(x^4 + 4*x^3 + 6*x^2 + 4*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264645, size = 62, normalized size = 2.21 \[ \frac{18 \, x^{2} + 3 \,{\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} \log \left (x + 1\right ) + 18 \, x + 8}{3 \,{\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/(x^4 + 4*x^3 + 6*x^2 + 4*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.231938, size = 29, normalized size = 1.04 \[ \frac{18 x^{2} + 18 x + 8}{3 x^{3} + 9 x^{2} + 9 x + 3} + \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-3*x**2+3*x-1)/(x**4+4*x**3+6*x**2+4*x+1),x)
[Out]
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GIAC/XCAS [A] time = 0.260213, size = 31, normalized size = 1.11 \[ \frac{2 \,{\left (9 \, x^{2} + 9 \, x + 4\right )}}{3 \,{\left (x + 1\right )}^{3}} +{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/(x^4 + 4*x^3 + 6*x^2 + 4*x + 1),x, algorithm="giac")
[Out]