3.486 \(\int \frac{7-2 x+3 x^2-x^3+x^4}{2+x} \, dx\)

Optimal. Leaf size=29 \[ \frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2) \]

[Out]

-20*x + (9*x^2)/2 - x^3 + x^4/4 + 47*Log[2 + x]

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Rubi [A]  time = 0.0425133, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2) \]

Antiderivative was successfully verified.

[In]  Int[(7 - 2*x + 3*x^2 - x^3 + x^4)/(2 + x),x]

[Out]

-20*x + (9*x^2)/2 - x^3 + x^4/4 + 47*Log[2 + x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{4}}{4} - x^{3} - 20 x + 47 \log{\left (x + 2 \right )} + 9 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**4-x**3+3*x**2-2*x+7)/(2+x),x)

[Out]

x**4/4 - x**3 - 20*x + 47*log(x + 2) + 9*Integral(x, x)

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Mathematica [A]  time = 0.0130473, size = 30, normalized size = 1.03 \[ \frac{x^4}{4}-x^3+\frac{9 x^2}{2}-20 x+47 \log (x+2)-70 \]

Antiderivative was successfully verified.

[In]  Integrate[(7 - 2*x + 3*x^2 - x^3 + x^4)/(2 + x),x]

[Out]

-70 - 20*x + (9*x^2)/2 - x^3 + x^4/4 + 47*Log[2 + x]

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Maple [A]  time = 0.003, size = 26, normalized size = 0.9 \[ -20\,x+{\frac{9\,{x}^{2}}{2}}-{x}^{3}+{\frac{{x}^{4}}{4}}+47\,\ln \left ( 2+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^4-x^3+3*x^2-2*x+7)/(2+x),x)

[Out]

-20*x+9/2*x^2-x^3+1/4*x^4+47*ln(2+x)

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Maxima [A]  time = 0.795033, size = 34, normalized size = 1.17 \[ \frac{1}{4} \, x^{4} - x^{3} + \frac{9}{2} \, x^{2} - 20 \, x + 47 \, \log \left (x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - x^3 + 3*x^2 - 2*x + 7)/(x + 2),x, algorithm="maxima")

[Out]

1/4*x^4 - x^3 + 9/2*x^2 - 20*x + 47*log(x + 2)

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Fricas [A]  time = 0.25018, size = 34, normalized size = 1.17 \[ \frac{1}{4} \, x^{4} - x^{3} + \frac{9}{2} \, x^{2} - 20 \, x + 47 \, \log \left (x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - x^3 + 3*x^2 - 2*x + 7)/(x + 2),x, algorithm="fricas")

[Out]

1/4*x^4 - x^3 + 9/2*x^2 - 20*x + 47*log(x + 2)

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Sympy [A]  time = 0.13882, size = 24, normalized size = 0.83 \[ \frac{x^{4}}{4} - x^{3} + \frac{9 x^{2}}{2} - 20 x + 47 \log{\left (x + 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**4-x**3+3*x**2-2*x+7)/(2+x),x)

[Out]

x**4/4 - x**3 + 9*x**2/2 - 20*x + 47*log(x + 2)

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GIAC/XCAS [A]  time = 0.259807, size = 35, normalized size = 1.21 \[ \frac{1}{4} \, x^{4} - x^{3} + \frac{9}{2} \, x^{2} - 20 \, x + 47 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - x^3 + 3*x^2 - 2*x + 7)/(x + 2),x, algorithm="giac")

[Out]

1/4*x^4 - x^3 + 9/2*x^2 - 20*x + 47*ln(abs(x + 2))