3.1347 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]

[Out]

(922*x)/243 - (1433*x^2)/162 + (82*x^3)/81 + (145*x^4)/9 - (40*x^5)/3 + (343*Log
[2 + 3*x])/729

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Rubi [A]  time = 0.0470103, antiderivative size = 44, 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 \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(922*x)/243 - (1433*x^2)/162 + (82*x^3)/81 + (145*x^4)/9 - (40*x^5)/3 + (343*Log
[2 + 3*x])/729

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{40 x^{5}}{3} + \frac{145 x^{4}}{9} + \frac{82 x^{3}}{81} + \frac{343 \log{\left (3 x + 2 \right )}}{729} + \int \frac{922}{243}\, dx - \frac{1433 \int x\, dx}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40*x**5/3 + 145*x**4/9 + 82*x**3/81 + 343*log(3*x + 2)/729 + Integral(922/243,
x) - 1433*Integral(x, x)/81

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Mathematica [A]  time = 0.0185504, size = 37, normalized size = 0.84 \[ \frac{-58320 x^5+70470 x^4+4428 x^3-38691 x^2+16596 x+2058 \log (3 x+2)+7972}{4374} \]

Antiderivative was successfully verified.

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

[Out]

(7972 + 16596*x - 38691*x^2 + 4428*x^3 + 70470*x^4 - 58320*x^5 + 2058*Log[2 + 3*
x])/4374

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Maple [A]  time = 0.004, size = 33, normalized size = 0.8 \[{\frac{922\,x}{243}}-{\frac{1433\,{x}^{2}}{162}}+{\frac{82\,{x}^{3}}{81}}+{\frac{145\,{x}^{4}}{9}}-{\frac{40\,{x}^{5}}{3}}+{\frac{343\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*ln(2+3*x)

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Maxima [A]  time = 1.37053, size = 43, normalized size = 0.98 \[ -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(3*x +
2)

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Fricas [A]  time = 0.208725, size = 43, normalized size = 0.98 \[ -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(3*x +
2)

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Sympy [A]  time = 0.184083, size = 41, normalized size = 0.93 \[ - \frac{40 x^{5}}{3} + \frac{145 x^{4}}{9} + \frac{82 x^{3}}{81} - \frac{1433 x^{2}}{162} + \frac{922 x}{243} + \frac{343 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40*x**5/3 + 145*x**4/9 + 82*x**3/81 - 1433*x**2/162 + 922*x/243 + 343*log(3*x +
2)/729

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GIAC/XCAS [A]  time = 0.205903, size = 45, normalized size = 1.02 \[ -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*ln(abs(3*
x + 2))