3.1372 \(\int \frac{(1-2 x)^3 (2+3 x)^5}{3+5 x} \, dx\)

Optimal. Leaf size=65 \[ -\frac{243 x^8}{5}-\frac{11988 x^7}{175}+\frac{4419 x^6}{125}+\frac{243333 x^5}{3125}-\frac{73749 x^4}{12500}-\frac{1703753 x^3}{46875}-\frac{138741 x^2}{156250}+\frac{4166223 x}{390625}+\frac{1331 \log (5 x+3)}{1953125} \]

[Out]

(4166223*x)/390625 - (138741*x^2)/156250 - (1703753*x^3)/46875 - (73749*x^4)/125
00 + (243333*x^5)/3125 + (4419*x^6)/125 - (11988*x^7)/175 - (243*x^8)/5 + (1331*
Log[3 + 5*x])/1953125

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Rubi [A]  time = 0.0654855, antiderivative size = 65, 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 \[ -\frac{243 x^8}{5}-\frac{11988 x^7}{175}+\frac{4419 x^6}{125}+\frac{243333 x^5}{3125}-\frac{73749 x^4}{12500}-\frac{1703753 x^3}{46875}-\frac{138741 x^2}{156250}+\frac{4166223 x}{390625}+\frac{1331 \log (5 x+3)}{1953125} \]

Antiderivative was successfully verified.

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

[Out]

(4166223*x)/390625 - (138741*x^2)/156250 - (1703753*x^3)/46875 - (73749*x^4)/125
00 + (243333*x^5)/3125 + (4419*x^6)/125 - (11988*x^7)/175 - (243*x^8)/5 + (1331*
Log[3 + 5*x])/1953125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{243 x^{8}}{5} - \frac{11988 x^{7}}{175} + \frac{4419 x^{6}}{125} + \frac{243333 x^{5}}{3125} - \frac{73749 x^{4}}{12500} - \frac{1703753 x^{3}}{46875} + \frac{1331 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{4166223}{390625}\, dx - \frac{138741 \int x\, dx}{78125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**8/5 - 11988*x**7/175 + 4419*x**6/125 + 243333*x**5/3125 - 73749*x**4/125
00 - 1703753*x**3/46875 + 1331*log(5*x + 3)/1953125 + Integral(4166223/390625, x
) - 138741*Integral(x, x)/78125

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Mathematica [A]  time = 0.021379, size = 52, normalized size = 0.8 \[ \frac{-39867187500 x^8-56193750000 x^7+28999687500 x^6+63874912500 x^5-4839778125 x^4-29815677500 x^3-728390250 x^2+8749068300 x+559020 \log (5 x+3)[phone]}{820312500} \]

Antiderivative was successfully verified.

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

[Out]

(2409164451 + 8749068300*x - 728390250*x^2 - 29815677500*x^3 - 4839778125*x^4 +
63874912500*x^5 + 28999687500*x^6 - 56193750000*x^7 - 39867187500*x^8 + 559020*L
og[3 + 5*x])/820312500

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Maple [A]  time = 0.003, size = 48, normalized size = 0.7 \[{\frac{4166223\,x}{390625}}-{\frac{138741\,{x}^{2}}{156250}}-{\frac{1703753\,{x}^{3}}{46875}}-{\frac{73749\,{x}^{4}}{12500}}+{\frac{243333\,{x}^{5}}{3125}}+{\frac{4419\,{x}^{6}}{125}}-{\frac{11988\,{x}^{7}}{175}}-{\frac{243\,{x}^{8}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{1953125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4166223/390625*x-138741/156250*x^2-1703753/46875*x^3-73749/12500*x^4+243333/3125
*x^5+4419/125*x^6-11988/175*x^7-243/5*x^8+1331/1953125*ln(3+5*x)

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Maxima [A]  time = 1.34331, size = 63, normalized size = 0.97 \[ -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/5*x^8 - 11988/175*x^7 + 4419/125*x^6 + 243333/3125*x^5 - 73749/12500*x^4 -
1703753/46875*x^3 - 138741/156250*x^2 + 4166223/390625*x + 1331/1953125*log(5*x
+ 3)

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Fricas [A]  time = 0.201237, size = 63, normalized size = 0.97 \[ -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/5*x^8 - 11988/175*x^7 + 4419/125*x^6 + 243333/3125*x^5 - 73749/12500*x^4 -
1703753/46875*x^3 - 138741/156250*x^2 + 4166223/390625*x + 1331/1953125*log(5*x
+ 3)

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Sympy [A]  time = 0.208643, size = 61, normalized size = 0.94 \[ - \frac{243 x^{8}}{5} - \frac{11988 x^{7}}{175} + \frac{4419 x^{6}}{125} + \frac{243333 x^{5}}{3125} - \frac{73749 x^{4}}{12500} - \frac{1703753 x^{3}}{46875} - \frac{138741 x^{2}}{156250} + \frac{4166223 x}{390625} + \frac{1331 \log{\left (5 x + 3 \right )}}{1953125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**8/5 - 11988*x**7/175 + 4419*x**6/125 + 243333*x**5/3125 - 73749*x**4/125
00 - 1703753*x**3/46875 - 138741*x**2/156250 + 4166223*x/390625 + 1331*log(5*x +
3)/1953125

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GIAC/XCAS [A]  time = 0.213512, size = 65, normalized size = 1. \[ -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/5*x^8 - 11988/175*x^7 + 4419/125*x^6 + 243333/3125*x^5 - 73749/12500*x^4 -
1703753/46875*x^3 - 138741/156250*x^2 + 4166223/390625*x + 1331/1953125*ln(abs(5
*x + 3))