3.1390 \(\int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=48 \[ -\frac{18 x^4}{25}+\frac{164 x^3}{125}-\frac{427 x^2}{625}-\frac{1179 x}{3125}-\frac{1331}{15625 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125} \]

[Out]

(-1179*x)/3125 - (427*x^2)/625 + (164*x^3)/125 - (18*x^4)/25 - 1331/(15625*(3 +
5*x)) + (1452*Log[3 + 5*x])/3125

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Rubi [A]  time = 0.061814, antiderivative size = 48, 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 \[ -\frac{18 x^4}{25}+\frac{164 x^3}{125}-\frac{427 x^2}{625}-\frac{1179 x}{3125}-\frac{1331}{15625 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(-1179*x)/3125 - (427*x^2)/625 + (164*x^3)/125 - (18*x^4)/25 - 1331/(15625*(3 +
5*x)) + (1452*Log[3 + 5*x])/3125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{18 x^{4}}{25} + \frac{164 x^{3}}{125} + \frac{1452 \log{\left (5 x + 3 \right )}}{3125} + \int \left (- \frac{1179}{3125}\right )\, dx - \frac{854 \int x\, dx}{625} - \frac{1331}{15625 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x**4/25 + 164*x**3/125 + 1452*log(5*x + 3)/3125 + Integral(-1179/3125, x) -
854*Integral(x, x)/625 - 1331/(15625*(5*x + 3))

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Mathematica [A]  time = 0.0478151, size = 51, normalized size = 1.06 \[ \frac{-11250 x^5+13750 x^4+1625 x^3-12300 x^2+2655 x+1452 (5 x+3) \log (6 (5 x+3))+3449}{3125 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(3449 + 2655*x - 12300*x^2 + 1625*x^3 + 13750*x^4 - 11250*x^5 + 1452*(3 + 5*x)*L
og[6*(3 + 5*x)])/(3125*(3 + 5*x))

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Maple [A]  time = 0.01, size = 37, normalized size = 0.8 \[ -{\frac{1179\,x}{3125}}-{\frac{427\,{x}^{2}}{625}}+{\frac{164\,{x}^{3}}{125}}-{\frac{18\,{x}^{4}}{25}}-{\frac{1331}{46875+78125\,x}}+{\frac{1452\,\ln \left ( 3+5\,x \right ) }{3125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1179/3125*x-427/625*x^2+164/125*x^3-18/25*x^4-1331/15625/(3+5*x)+1452/3125*ln(3
+5*x)

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Maxima [A]  time = 1.34877, size = 49, normalized size = 1.02 \[ -\frac{18}{25} \, x^{4} + \frac{164}{125} \, x^{3} - \frac{427}{625} \, x^{2} - \frac{1179}{3125} \, x - \frac{1331}{15625 \,{\left (5 \, x + 3\right )}} + \frac{1452}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18/25*x^4 + 164/125*x^3 - 427/625*x^2 - 1179/3125*x - 1331/15625/(5*x + 3) + 14
52/3125*log(5*x + 3)

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Fricas [A]  time = 0.203815, size = 63, normalized size = 1.31 \[ -\frac{56250 \, x^{5} - 68750 \, x^{4} - 8125 \, x^{3} + 61500 \, x^{2} - 7260 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 17685 \, x + 1331}{15625 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15625*(56250*x^5 - 68750*x^4 - 8125*x^3 + 61500*x^2 - 7260*(5*x + 3)*log(5*x
+ 3) + 17685*x + 1331)/(5*x + 3)

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Sympy [A]  time = 0.238297, size = 41, normalized size = 0.85 \[ - \frac{18 x^{4}}{25} + \frac{164 x^{3}}{125} - \frac{427 x^{2}}{625} - \frac{1179 x}{3125} + \frac{1452 \log{\left (5 x + 3 \right )}}{3125} - \frac{1331}{78125 x + 46875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x**4/25 + 164*x**3/125 - 427*x**2/625 - 1179*x/3125 + 1452*log(5*x + 3)/3125
- 1331/(78125*x + 46875)

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GIAC/XCAS [A]  time = 0.210351, size = 89, normalized size = 1.85 \[ \frac{1}{15625} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{380}{5 \, x + 3} - \frac{2875}{{\left (5 \, x + 3\right )}^{2}} + \frac{7755}{{\left (5 \, x + 3\right )}^{3}} - 18\right )} - \frac{1331}{15625 \,{\left (5 \, x + 3\right )}} - \frac{1452}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/15625*(5*x + 3)^4*(380/(5*x + 3) - 2875/(5*x + 3)^2 + 7755/(5*x + 3)^3 - 18) -
1331/15625/(5*x + 3) - 1452/3125*ln(1/5*abs(5*x + 3)/(5*x + 3)^2)