3.1308 \(\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=59 \[ \frac{81 x^4}{125}-\frac{72 x^3}{625}-\frac{4779 x^2}{6250}+\frac{1419 x}{3125}-\frac{1408}{78125 (5 x+3)}-\frac{121}{156250 (5 x+3)^2}+\frac{1202 \log (5 x+3)}{15625} \]

[Out]

(1419*x)/3125 - (4779*x^2)/6250 - (72*x^3)/625 + (81*x^4)/125 - 121/(156250*(3 +
5*x)^2) - 1408/(78125*(3 + 5*x)) + (1202*Log[3 + 5*x])/15625

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Rubi [A]  time = 0.0745244, antiderivative size = 59, 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 \[ \frac{81 x^4}{125}-\frac{72 x^3}{625}-\frac{4779 x^2}{6250}+\frac{1419 x}{3125}-\frac{1408}{78125 (5 x+3)}-\frac{121}{156250 (5 x+3)^2}+\frac{1202 \log (5 x+3)}{15625} \]

Antiderivative was successfully verified.

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

[Out]

(1419*x)/3125 - (4779*x^2)/6250 - (72*x^3)/625 + (81*x^4)/125 - 121/(156250*(3 +
5*x)^2) - 1408/(78125*(3 + 5*x)) + (1202*Log[3 + 5*x])/15625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{81 x^{4}}{125} - \frac{72 x^{3}}{625} + \frac{1202 \log{\left (5 x + 3 \right )}}{15625} + \int \frac{1419}{3125}\, dx - \frac{4779 \int x\, dx}{3125} - \frac{1408}{78125 \left (5 x + 3\right )} - \frac{121}{156250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81*x**4/125 - 72*x**3/625 + 1202*log(5*x + 3)/15625 + Integral(1419/3125, x) - 4
779*Integral(x, x)/3125 - 1408/(78125*(5*x + 3)) - 121/(156250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0521019, size = 58, normalized size = 0.98 \[ \frac{506250 x^6+517500 x^5-523125 x^4-394500 x^3+553500 x^2+536320 x+2404 (5 x+3)^2 \log (6 (5 x+3))+121714}{31250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(121714 + 536320*x + 553500*x^2 - 394500*x^3 - 523125*x^4 + 517500*x^5 + 506250*
x^6 + 2404*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(31250*(3 + 5*x)^2)

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Maple [A]  time = 0.009, size = 46, normalized size = 0.8 \[{\frac{1419\,x}{3125}}-{\frac{4779\,{x}^{2}}{6250}}-{\frac{72\,{x}^{3}}{625}}+{\frac{81\,{x}^{4}}{125}}-{\frac{121}{156250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{1408}{234375+390625\,x}}+{\frac{1202\,\ln \left ( 3+5\,x \right ) }{15625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1419/3125*x-4779/6250*x^2-72/625*x^3+81/125*x^4-121/156250/(3+5*x)^2-1408/78125/
(3+5*x)+1202/15625*ln(3+5*x)

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Maxima [A]  time = 1.34793, size = 62, normalized size = 1.05 \[ \frac{81}{125} \, x^{4} - \frac{72}{625} \, x^{3} - \frac{4779}{6250} \, x^{2} + \frac{1419}{3125} \, x - \frac{11 \,{\left (1280 \, x + 779\right )}}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{1202}{15625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/125*x^4 - 72/625*x^3 - 4779/6250*x^2 + 1419/3125*x - 11/156250*(1280*x + 779)
/(25*x^2 + 30*x + 9) + 1202/15625*log(5*x + 3)

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Fricas [A]  time = 0.218208, size = 84, normalized size = 1.42 \[ \frac{2531250 \, x^{6} + 2587500 \, x^{5} - 2615625 \, x^{4} - 1972500 \, x^{3} + 1053225 \, x^{2} + 12020 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 624470 \, x - 8569}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/156250*(2531250*x^6 + 2587500*x^5 - 2615625*x^4 - 1972500*x^3 + 1053225*x^2 +
12020*(25*x^2 + 30*x + 9)*log(5*x + 3) + 624470*x - 8569)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.29909, size = 49, normalized size = 0.83 \[ \frac{81 x^{4}}{125} - \frac{72 x^{3}}{625} - \frac{4779 x^{2}}{6250} + \frac{1419 x}{3125} - \frac{14080 x + 8569}{3906250 x^{2} + 4687500 x + 1406250} + \frac{1202 \log{\left (5 x + 3 \right )}}{15625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81*x**4/125 - 72*x**3/625 - 4779*x**2/6250 + 1419*x/3125 - (14080*x + 8569)/(390
6250*x**2 + 4687500*x + 1406250) + 1202*log(5*x + 3)/15625

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GIAC/XCAS [A]  time = 0.216228, size = 57, normalized size = 0.97 \[ \frac{81}{125} \, x^{4} - \frac{72}{625} \, x^{3} - \frac{4779}{6250} \, x^{2} + \frac{1419}{3125} \, x - \frac{11 \,{\left (1280 \, x + 779\right )}}{156250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{1202}{15625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/125*x^4 - 72/625*x^3 - 4779/6250*x^2 + 1419/3125*x - 11/156250*(1280*x + 779)
/(5*x + 3)^2 + 1202/15625*ln(abs(5*x + 3))