3.1228 \(\int \frac{(1-2 x)^2 (3+5 x)}{2+3 x} \, dx\)

Optimal. Leaf size=30 \[ \frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2) \]

[Out]

(65*x)/27 - (32*x^2)/9 + (20*x^3)/9 - (49*Log[2 + 3*x])/81

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Rubi [A]  time = 0.0318255, antiderivative size = 30, 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 \[ \frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(65*x)/27 - (32*x^2)/9 + (20*x^3)/9 - (49*Log[2 + 3*x])/81

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{20 x^{3}}{9} - \frac{49 \log{\left (3 x + 2 \right )}}{81} + \int \frac{65}{27}\, dx - \frac{64 \int x\, dx}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x**3/9 - 49*log(3*x + 2)/81 + Integral(65/27, x) - 64*Integral(x, x)/9

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Mathematica [A]  time = 0.0149019, size = 27, normalized size = 0.9 \[ \frac{1}{243} \left (540 x^3-864 x^2+585 x-147 \log (3 x+2)+934\right ) \]

Antiderivative was successfully verified.

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

[Out]

(934 + 585*x - 864*x^2 + 540*x^3 - 147*Log[2 + 3*x])/243

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Maple [A]  time = 0.003, size = 23, normalized size = 0.8 \[{\frac{65\,x}{27}}-{\frac{32\,{x}^{2}}{9}}+{\frac{20\,{x}^{3}}{9}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

65/27*x-32/9*x^2+20/9*x^3-49/81*ln(2+3*x)

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Maxima [A]  time = 1.34465, size = 30, normalized size = 1. \[ \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/9*x^3 - 32/9*x^2 + 65/27*x - 49/81*log(3*x + 2)

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Fricas [A]  time = 0.211904, size = 30, normalized size = 1. \[ \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/9*x^3 - 32/9*x^2 + 65/27*x - 49/81*log(3*x + 2)

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Sympy [A]  time = 0.154835, size = 27, normalized size = 0.9 \[ \frac{20 x^{3}}{9} - \frac{32 x^{2}}{9} + \frac{65 x}{27} - \frac{49 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x**3/9 - 32*x**2/9 + 65*x/27 - 49*log(3*x + 2)/81

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GIAC/XCAS [A]  time = 0.205062, size = 31, normalized size = 1.03 \[ \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/9*x^3 - 32/9*x^2 + 65/27*x - 49/81*ln(abs(3*x + 2))