3.2378 \(\int \frac{(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx\)

Optimal. Leaf size=36 \[ -\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2) \]

[Out]

(922*x)/27 + (26*x^2)/9 - (8*x^3)/9 - 6*Log[1 + x] + (2125*Log[2 + 3*x])/81

_______________________________________________________________________________________

Rubi [A]  time = 0.0584027, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.12 \[ -\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2),x]

[Out]

(922*x)/27 + (26*x^2)/9 - (8*x^3)/9 - 6*Log[1 + x] + (2125*Log[2 + 3*x])/81

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{8 x^{3}}{9} - 6 \log{\left (x + 1 \right )} + \frac{2125 \log{\left (3 x + 2 \right )}}{81} + \int \frac{922}{27}\, dx + \frac{52 \int x\, dx}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2),x)

[Out]

-8*x**3/9 - 6*log(x + 1) + 2125*log(3*x + 2)/81 + Integral(922/27, x) + 52*Integ
ral(x, x)/9

_______________________________________________________________________________________

Mathematica [A]  time = 0.027843, size = 35, normalized size = 0.97 \[ \frac{1}{162} \left (-144 x^3+468 x^2+5532 x+4250 \log (-6 x-4)-972 \log (-2 (x+1))+6759\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2),x]

[Out]

(6759 + 5532*x + 468*x^2 - 144*x^3 + 4250*Log[-4 - 6*x] - 972*Log[-2*(1 + x)])/1
62

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 29, normalized size = 0.8 \[{\frac{922\,x}{27}}+{\frac{26\,{x}^{2}}{9}}-{\frac{8\,{x}^{3}}{9}}-6\,\ln \left ( 1+x \right ) +{\frac{2125\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((5-x)*(3+2*x)^3/(3*x^2+5*x+2),x)

[Out]

922/27*x+26/9*x^2-8/9*x^3-6*ln(1+x)+2125/81*ln(2+3*x)

_______________________________________________________________________________________

Maxima [A]  time = 0.689917, size = 38, normalized size = 1.06 \[ -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2),x, algorithm="maxima")

[Out]

-8/9*x^3 + 26/9*x^2 + 922/27*x + 2125/81*log(3*x + 2) - 6*log(x + 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.279744, size = 38, normalized size = 1.06 \[ -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2),x, algorithm="fricas")

[Out]

-8/9*x^3 + 26/9*x^2 + 922/27*x + 2125/81*log(3*x + 2) - 6*log(x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.272188, size = 34, normalized size = 0.94 \[ - \frac{8 x^{3}}{9} + \frac{26 x^{2}}{9} + \frac{922 x}{27} + \frac{2125 \log{\left (x + \frac{2}{3} \right )}}{81} - 6 \log{\left (x + 1 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2),x)

[Out]

-8*x**3/9 + 26*x**2/9 + 922*x/27 + 2125*log(x + 2/3)/81 - 6*log(x + 1)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.293626, size = 41, normalized size = 1.14 \[ -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - 6 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2),x, algorithm="giac")

[Out]

-8/9*x^3 + 26/9*x^2 + 922/27*x + 2125/81*ln(abs(3*x + 2)) - 6*ln(abs(x + 1))