3.1291 \(\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{324 x^5}{125}+\frac{189 x^4}{125}-\frac{1809 x^3}{625}-\frac{3621 x^2}{3125}+\frac{5459 x}{3125}-\frac{121}{78125 (5 x+3)}+\frac{1408 \log (5 x+3)}{78125} \]

[Out]

(5459*x)/3125 - (3621*x^2)/3125 - (1809*x^3)/625 + (189*x^4)/125 + (324*x^5)/125
- 121/(78125*(3 + 5*x)) + (1408*Log[3 + 5*x])/78125

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Rubi [A]  time = 0.0687483, antiderivative size = 55, 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 \[ \frac{324 x^5}{125}+\frac{189 x^4}{125}-\frac{1809 x^3}{625}-\frac{3621 x^2}{3125}+\frac{5459 x}{3125}-\frac{121}{78125 (5 x+3)}+\frac{1408 \log (5 x+3)}{78125} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^2,x]

[Out]

(5459*x)/3125 - (3621*x^2)/3125 - (1809*x^3)/625 + (189*x^4)/125 + (324*x^5)/125
- 121/(78125*(3 + 5*x)) + (1408*Log[3 + 5*x])/78125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{324 x^{5}}{125} + \frac{189 x^{4}}{125} - \frac{1809 x^{3}}{625} + \frac{1408 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{5459}{3125}\, dx - \frac{7242 \int x\, dx}{3125} - \frac{121}{78125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**4/(3+5*x)**2,x)

[Out]

324*x**5/125 + 189*x**4/125 - 1809*x**3/625 + 1408*log(5*x + 3)/78125 + Integral
(5459/3125, x) - 7242*Integral(x, x)/3125 - 121/(78125*(5*x + 3))

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Mathematica [A]  time = 0.0510274, size = 56, normalized size = 1.02 \[ \frac{5062500 x^6+5990625 x^5-3881250 x^4-5655000 x^3+2054000 x^2+3698835 x+7040 (5 x+3) \log (6 (5 x+3))+990421}{390625 (5 x+3)} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^2,x]

[Out]

(990421 + 3698835*x + 2054000*x^2 - 5655000*x^3 - 3881250*x^4 + 5990625*x^5 + 50
62500*x^6 + 7040*(3 + 5*x)*Log[6*(3 + 5*x)])/(390625*(3 + 5*x))

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Maple [A]  time = 0.008, size = 42, normalized size = 0.8 \[{\frac{5459\,x}{3125}}-{\frac{3621\,{x}^{2}}{3125}}-{\frac{1809\,{x}^{3}}{625}}+{\frac{189\,{x}^{4}}{125}}+{\frac{324\,{x}^{5}}{125}}-{\frac{121}{234375+390625\,x}}+{\frac{1408\,\ln \left ( 3+5\,x \right ) }{78125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^4/(3+5*x)^2,x)

[Out]

5459/3125*x-3621/3125*x^2-1809/625*x^3+189/125*x^4+324/125*x^5-121/78125/(3+5*x)
+1408/78125*ln(3+5*x)

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Maxima [A]  time = 1.34091, size = 55, normalized size = 1. \[ \frac{324}{125} \, x^{5} + \frac{189}{125} \, x^{4} - \frac{1809}{625} \, x^{3} - \frac{3621}{3125} \, x^{2} + \frac{5459}{3125} \, x - \frac{121}{78125 \,{\left (5 \, x + 3\right )}} + \frac{1408}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")

[Out]

324/125*x^5 + 189/125*x^4 - 1809/625*x^3 - 3621/3125*x^2 + 5459/3125*x - 121/781
25/(5*x + 3) + 1408/78125*log(5*x + 3)

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Fricas [A]  time = 0.216817, size = 70, normalized size = 1.27 \[ \frac{1012500 \, x^{6} + 1198125 \, x^{5} - 776250 \, x^{4} - 1131000 \, x^{3} + 410800 \, x^{2} + 1408 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 409425 \, x - 121}{78125 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")

[Out]

1/78125*(1012500*x^6 + 1198125*x^5 - 776250*x^4 - 1131000*x^3 + 410800*x^2 + 140
8*(5*x + 3)*log(5*x + 3) + 409425*x - 121)/(5*x + 3)

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Sympy [A]  time = 0.248456, size = 48, normalized size = 0.87 \[ \frac{324 x^{5}}{125} + \frac{189 x^{4}}{125} - \frac{1809 x^{3}}{625} - \frac{3621 x^{2}}{3125} + \frac{5459 x}{3125} + \frac{1408 \log{\left (5 x + 3 \right )}}{78125} - \frac{121}{390625 x + 234375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**4/(3+5*x)**2,x)

[Out]

324*x**5/125 + 189*x**4/125 - 1809*x**3/625 - 3621*x**2/3125 + 5459*x/3125 + 140
8*log(5*x + 3)/78125 - 121/(390625*x + 234375)

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GIAC/XCAS [A]  time = 0.212559, size = 101, normalized size = 1.84 \[ -\frac{1}{390625} \,{\left (5 \, x + 3\right )}^{5}{\left (\frac{3915}{5 \, x + 3} - \frac{8775}{{\left (5 \, x + 3\right )}^{2}} - \frac{26850}{{\left (5 \, x + 3\right )}^{3}} - \frac{30050}{{\left (5 \, x + 3\right )}^{4}} - 324\right )} - \frac{121}{78125 \,{\left (5 \, x + 3\right )}} - \frac{1408}{78125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")

[Out]

-1/390625*(5*x + 3)^5*(3915/(5*x + 3) - 8775/(5*x + 3)^2 - 26850/(5*x + 3)^3 - 3
0050/(5*x + 3)^4 - 324) - 121/78125/(5*x + 3) - 1408/78125*ln(1/5*abs(5*x + 3)/(
5*x + 3)^2)