3.1363 \(\int \frac{(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187} \]

[Out]

(10013*x)/729 - (8287*x^2)/486 - (6427*x^3)/243 + (2815*x^4)/54 + (220*x^5)/9 -
(500*x^6)/9 - (343*Log[2 + 3*x])/2187

_______________________________________________________________________________________

Rubi [A]  time = 0.0533533, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x),x]

[Out]

(10013*x)/729 - (8287*x^2)/486 - (6427*x^3)/243 + (2815*x^4)/54 + (220*x^5)/9 -
(500*x^6)/9 - (343*Log[2 + 3*x])/2187

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{500 x^{6}}{9} + \frac{220 x^{5}}{9} + \frac{2815 x^{4}}{54} - \frac{6427 x^{3}}{243} - \frac{343 \log{\left (3 x + 2 \right )}}{2187} + \int \frac{10013}{729}\, dx - \frac{8287 \int x\, dx}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)**3/(2+3*x),x)

[Out]

-500*x**6/9 + 220*x**5/9 + 2815*x**4/54 - 6427*x**3/243 - 343*log(3*x + 2)/2187
+ Integral(10013/729, x) - 8287*Integral(x, x)/243

_______________________________________________________________________________________

Mathematica [A]  time = 0.0194009, size = 42, normalized size = 0.82 \[ \frac{-243000 x^6+106920 x^5+228015 x^4-115686 x^3-74583 x^2+60078 x-686 \log (3 x+2)+29296}{4374} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x),x]

[Out]

(29296 + 60078*x - 74583*x^2 - 115686*x^3 + 228015*x^4 + 106920*x^5 - 243000*x^6
- 686*Log[2 + 3*x])/4374

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 38, normalized size = 0.8 \[{\frac{10013\,x}{729}}-{\frac{8287\,{x}^{2}}{486}}-{\frac{6427\,{x}^{3}}{243}}+{\frac{2815\,{x}^{4}}{54}}+{\frac{220\,{x}^{5}}{9}}-{\frac{500\,{x}^{6}}{9}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{2187}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)^3/(2+3*x),x)

[Out]

10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-343/2187*l
n(2+3*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33265, size = 50, normalized size = 0.98 \[ -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2),x, algorithm="maxima")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x
- 343/2187*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.203455, size = 50, normalized size = 0.98 \[ -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2),x, algorithm="fricas")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x
- 343/2187*log(3*x + 2)

_______________________________________________________________________________________

Sympy [A]  time = 0.180223, size = 48, normalized size = 0.94 \[ - \frac{500 x^{6}}{9} + \frac{220 x^{5}}{9} + \frac{2815 x^{4}}{54} - \frac{6427 x^{3}}{243} - \frac{8287 x^{2}}{486} + \frac{10013 x}{729} - \frac{343 \log{\left (3 x + 2 \right )}}{2187} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)**3/(2+3*x),x)

[Out]

-500*x**6/9 + 220*x**5/9 + 2815*x**4/54 - 6427*x**3/243 - 8287*x**2/486 + 10013*
x/729 - 343*log(3*x + 2)/2187

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210992, size = 51, normalized size = 1. \[ -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)^3/(3*x + 2),x, algorithm="giac")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x
- 343/2187*ln(abs(3*x + 2))