3.266 \(\int \frac{1+x^3}{-2+x} \, dx\)

Optimal. Leaf size=22 \[ \frac{x^3}{3}+x^2+4 x+9 \log (2-x) \]

[Out]

4*x + x^2 + x^3/3 + 9*Log[2 - x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0316454, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^3}{3}+x^2+4 x+9 \log (2-x) \]

Antiderivative was successfully verified.

[In]  Int[(1 + x^3)/(-2 + x),x]

[Out]

4*x + x^2 + x^3/3 + 9*Log[2 - x]

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**3+1)/(-2+x),x)

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.0063875, size = 23, normalized size = 1.05 \[ \frac{x^3}{3}+x^2+4 x+9 \log (x-2)-\frac{44}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + x^3)/(-2 + x),x]

[Out]

-44/3 + 4*x + x^2 + x^3/3 + 9*Log[-2 + x]

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 19, normalized size = 0.9 \[{\frac{{x}^{3}}{3}}+{x}^{2}+4\,x+9\,\ln \left ( x-2 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^3+1)/(x-2),x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 0.813851, size = 24, normalized size = 1.09 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 1)/(x - 2),x, algorithm="maxima")

[Out]

1/3*x^3 + x^2 + 4*x + 9*log(x - 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.262207, size = 24, normalized size = 1.09 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 1)/(x - 2),x, algorithm="fricas")

[Out]

1/3*x^3 + x^2 + 4*x + 9*log(x - 2)

_______________________________________________________________________________________

Sympy [A]  time = 0.114196, size = 17, normalized size = 0.77 \[ \frac{x^{3}}{3} + x^{2} + 4 x + 9 \log{\left (x - 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**3+1)/(-2+x),x)

[Out]

x**3/3 + x**2 + 4*x + 9*log(x - 2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.259357, size = 26, normalized size = 1.18 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 1)/(x - 2),x, algorithm="giac")

[Out]

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