3.1391 \(\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=41 \[ -\frac{8 x^3}{25}+\frac{122 x^2}{125}-\frac{1098 x}{625}-\frac{1331}{3125 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125} \]

[Out]

(-1098*x)/625 + (122*x^2)/125 - (8*x^3)/25 - 1331/(3125*(3 + 5*x)) + (3267*Log[3
+ 5*x])/3125

_______________________________________________________________________________________

Rubi [A]  time = 0.0504898, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{8 x^3}{25}+\frac{122 x^2}{125}-\frac{1098 x}{625}-\frac{1331}{3125 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(-1098*x)/625 + (122*x^2)/125 - (8*x^3)/25 - 1331/(3125*(3 + 5*x)) + (3267*Log[3
+ 5*x])/3125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{8 x^{3}}{25} + \frac{3267 \log{\left (5 x + 3 \right )}}{3125} + \int \left (- \frac{1098}{625}\right )\, dx + \frac{244 \int x\, dx}{125} - \frac{1331}{3125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x**3/25 + 3267*log(5*x + 3)/3125 + Integral(-1098/625, x) + 244*Integral(x, x
)/125 - 1331/(3125*(5*x + 3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0223774, size = 44, normalized size = 1.07 \[ \frac{-10000 x^4+24500 x^3-36600 x^2-11865 x+6534 (5 x+3) \log (10 x+6)+9983}{6250 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(9983 - 11865*x - 36600*x^2 + 24500*x^3 - 10000*x^4 + 6534*(3 + 5*x)*Log[6 + 10*
x])/(6250*(3 + 5*x))

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 32, normalized size = 0.8 \[ -{\frac{1098\,x}{625}}+{\frac{122\,{x}^{2}}{125}}-{\frac{8\,{x}^{3}}{25}}-{\frac{1331}{9375+15625\,x}}+{\frac{3267\,\ln \left ( 3+5\,x \right ) }{3125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1098/625*x+122/125*x^2-8/25*x^3-1331/3125/(3+5*x)+3267/3125*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34764, size = 42, normalized size = 1.02 \[ -\frac{8}{25} \, x^{3} + \frac{122}{125} \, x^{2} - \frac{1098}{625} \, x - \frac{1331}{3125 \,{\left (5 \, x + 3\right )}} + \frac{3267}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/25*x^3 + 122/125*x^2 - 1098/625*x - 1331/3125/(5*x + 3) + 3267/3125*log(5*x +
3)

_______________________________________________________________________________________

Fricas [A]  time = 0.211148, size = 57, normalized size = 1.39 \[ -\frac{5000 \, x^{4} - 12250 \, x^{3} + 18300 \, x^{2} - 3267 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 16470 \, x + 1331}{3125 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3125*(5000*x^4 - 12250*x^3 + 18300*x^2 - 3267*(5*x + 3)*log(5*x + 3) + 16470*
x + 1331)/(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.223389, size = 34, normalized size = 0.83 \[ - \frac{8 x^{3}}{25} + \frac{122 x^{2}}{125} - \frac{1098 x}{625} + \frac{3267 \log{\left (5 x + 3 \right )}}{3125} - \frac{1331}{15625 x + 9375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x**3/25 + 122*x**2/125 - 1098*x/625 + 3267*log(5*x + 3)/3125 - 1331/(15625*x
+ 9375)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208265, size = 77, normalized size = 1.88 \[ \frac{2}{3125} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{97}{5 \, x + 3} - \frac{1023}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac{1331}{3125 \,{\left (5 \, x + 3\right )}} - \frac{3267}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/3125*(5*x + 3)^3*(97/(5*x + 3) - 1023/(5*x + 3)^2 - 4) - 1331/3125/(5*x + 3) -
3267/3125*ln(1/5*abs(5*x + 3)/(5*x + 3)^2)