3.1195 \(\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=34 \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]

[Out]

(33*x)/125 - (9*x^2)/25 - 11/(625*(3 + 5*x)) + (64*Log[3 + 5*x])/625

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Rubi [A]  time = 0.0448879, antiderivative size = 34, 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 \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(33*x)/125 - (9*x^2)/25 - 11/(625*(3 + 5*x)) + (64*Log[3 + 5*x])/625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{64 \log{\left (5 x + 3 \right )}}{625} + \int \frac{33}{125}\, dx - \frac{18 \int x\, dx}{25} - \frac{11}{625 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64*log(5*x + 3)/625 + Integral(33/125, x) - 18*Integral(x, x)/25 - 11/(625*(5*x
+ 3))

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Mathematica [A]  time = 0.0201884, size = 41, normalized size = 1.21 \[ \frac{-1125 x^3+150 x^2+1545 x+64 (5 x+3) \log (-3 (5 x+3))+619}{625 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(619 + 1545*x + 150*x^2 - 1125*x^3 + 64*(3 + 5*x)*Log[-3*(3 + 5*x)])/(625*(3 + 5
*x))

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Maple [A]  time = 0.01, size = 27, normalized size = 0.8 \[{\frac{33\,x}{125}}-{\frac{9\,{x}^{2}}{25}}-{\frac{11}{1875+3125\,x}}+{\frac{64\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

33/125*x-9/25*x^2-11/625/(3+5*x)+64/625*ln(3+5*x)

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Maxima [A]  time = 1.34209, size = 35, normalized size = 1.03 \[ -\frac{9}{25} \, x^{2} + \frac{33}{125} \, x - \frac{11}{625 \,{\left (5 \, x + 3\right )}} + \frac{64}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9/25*x^2 + 33/125*x - 11/625/(5*x + 3) + 64/625*log(5*x + 3)

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Fricas [A]  time = 0.218293, size = 50, normalized size = 1.47 \[ -\frac{1125 \, x^{3} - 150 \, x^{2} - 64 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 495 \, x + 11}{625 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/625*(1125*x^3 - 150*x^2 - 64*(5*x + 3)*log(5*x + 3) - 495*x + 11)/(5*x + 3)

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Sympy [A]  time = 0.199334, size = 27, normalized size = 0.79 \[ - \frac{9 x^{2}}{25} + \frac{33 x}{125} + \frac{64 \log{\left (5 x + 3 \right )}}{625} - \frac{11}{3125 x + 1875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9*x**2/25 + 33*x/125 + 64*log(5*x + 3)/625 - 11/(3125*x + 1875)

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GIAC/XCAS [A]  time = 0.212051, size = 65, normalized size = 1.91 \[ \frac{3}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{29}{5 \, x + 3} - 3\right )} - \frac{11}{625 \,{\left (5 \, x + 3\right )}} - \frac{64}{625} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/625*(5*x + 3)^2*(29/(5*x + 3) - 3) - 11/625/(5*x + 3) - 64/625*ln(1/5*abs(5*x
+ 3)/(5*x + 3)^2)