3.1277 \(\int \frac{(1-2 x)^2 (2+3 x)^2}{3+5 x} \, dx\)

Optimal. Leaf size=37 \[ \frac{9 x^4}{5}-\frac{16 x^3}{25}-\frac{431 x^2}{250}+\frac{793 x}{625}+\frac{121 \log (5 x+3)}{3125} \]

[Out]

(793*x)/625 - (431*x^2)/250 - (16*x^3)/25 + (9*x^4)/5 + (121*Log[3 + 5*x])/3125

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Rubi [A]  time = 0.0423977, antiderivative size = 37, 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 \[ \frac{9 x^4}{5}-\frac{16 x^3}{25}-\frac{431 x^2}{250}+\frac{793 x}{625}+\frac{121 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(793*x)/625 - (431*x^2)/250 - (16*x^3)/25 + (9*x^4)/5 + (121*Log[3 + 5*x])/3125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{9 x^{4}}{5} - \frac{16 x^{3}}{25} + \frac{121 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{793}{625}\, dx - \frac{431 \int x\, dx}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9*x**4/5 - 16*x**3/25 + 121*log(5*x + 3)/3125 + Integral(793/625, x) - 431*Integ
ral(x, x)/125

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Mathematica [A]  time = 0.0176346, size = 35, normalized size = 0.95 \[ \frac{5 \left (2250 x^4-800 x^3-2155 x^2+1586 x+1263\right )+242 \log (5 x+3)}{6250} \]

Antiderivative was successfully verified.

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

[Out]

(5*(1263 + 1586*x - 2155*x^2 - 800*x^3 + 2250*x^4) + 242*Log[3 + 5*x])/6250

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Maple [A]  time = 0.003, size = 28, normalized size = 0.8 \[{\frac{793\,x}{625}}-{\frac{431\,{x}^{2}}{250}}-{\frac{16\,{x}^{3}}{25}}+{\frac{9\,{x}^{4}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{3125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

793/625*x-431/250*x^2-16/25*x^3+9/5*x^4+121/3125*ln(3+5*x)

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Maxima [A]  time = 1.34357, size = 36, normalized size = 0.97 \[ \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9/5*x^4 - 16/25*x^3 - 431/250*x^2 + 793/625*x + 121/3125*log(5*x + 3)

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Fricas [A]  time = 0.210641, size = 36, normalized size = 0.97 \[ \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9/5*x^4 - 16/25*x^3 - 431/250*x^2 + 793/625*x + 121/3125*log(5*x + 3)

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Sympy [A]  time = 0.160911, size = 34, normalized size = 0.92 \[ \frac{9 x^{4}}{5} - \frac{16 x^{3}}{25} - \frac{431 x^{2}}{250} + \frac{793 x}{625} + \frac{121 \log{\left (5 x + 3 \right )}}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9*x**4/5 - 16*x**3/25 - 431*x**2/250 + 793*x/625 + 121*log(5*x + 3)/3125

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GIAC/XCAS [A]  time = 0.207374, size = 38, normalized size = 1.03 \[ \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9/5*x^4 - 16/25*x^3 - 431/250*x^2 + 793/625*x + 121/3125*ln(abs(5*x + 3))