3.1539 \(\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=69 \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]

[Out]

14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)
/64 + (575775*x^4)/16 + (1295919*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (123
86759*Log[1 - 2*x])/128

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Rubi [A]  time = 0.0885588, antiderivative size = 69, 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 \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^2,x]

[Out]

14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)
/64 + (575775*x^4)/16 + (1295919*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (123
86759*Log[1 - 2*x])/128

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{18225 x^{7}}{28} + \frac{37665 x^{6}}{8} + \frac{1295919 x^{5}}{80} + \frac{575775 x^{4}}{16} + \frac{3851307 x^{3}}{64} + \frac{12386759 \log{\left (- 2 x + 1 \right )}}{128} + \int \frac{35458963}{256}\, dx + \frac{11140101 \int x\, dx}{64} + \frac{14235529}{512 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6*(3+5*x)**2/(1-2*x)**2,x)

[Out]

18225*x**7/28 + 37665*x**6/8 + 1295919*x**5/80 + 575775*x**4/16 + 3851307*x**3/6
4 + 12386759*log(-2*x + 1)/128 + Integral(35458963/256, x) + 11140101*Integral(x
, x)/64 + 14235529/(512*(-2*x + 1))

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Mathematica [A]  time = 0.033547, size = 64, normalized size = 0.93 \[ \frac{23328000 x^8+157075200 x^7+496202112 x^6+999450144 x^5+1511863920 x^4+2040862320 x^3+3404640680 x^2-6115223546 x+1734146260 (2 x-1) \log (1-2 x)[phone]}{17920 (2 x-1)} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^2,x]

[Out]

(1318304553 - 6115223546*x + 3404640680*x^2 + 2040862320*x^3 + 1511863920*x^4 +
999450144*x^5 + 496202112*x^6 + 157075200*x^7 + 23328000*x^8 + 1734146260*(-1 +
2*x)*Log[1 - 2*x])/(17920*(-1 + 2*x))

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Maple [A]  time = 0.01, size = 52, normalized size = 0.8 \[{\frac{18225\,{x}^{7}}{28}}+{\frac{37665\,{x}^{6}}{8}}+{\frac{1295919\,{x}^{5}}{80}}+{\frac{575775\,{x}^{4}}{16}}+{\frac{3851307\,{x}^{3}}{64}}+{\frac{11140101\,{x}^{2}}{128}}+{\frac{35458963\,x}{256}}-{\frac{14235529}{-512+1024\,x}}+{\frac{12386759\,\ln \left ( -1+2\,x \right ) }{128}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6*(3+5*x)^2/(1-2*x)^2,x)

[Out]

18225/28*x^7+37665/8*x^6+1295919/80*x^5+575775/16*x^4+3851307/64*x^3+11140101/12
8*x^2+35458963/256*x-14235529/512/(-1+2*x)[phone]/128*ln(-1+2*x)

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Maxima [A]  time = 1.32793, size = 69, normalized size = 1. \[ \frac{18225}{28} \, x^{7} + \frac{37665}{8} \, x^{6} + \frac{1295919}{80} \, x^{5} + \frac{575775}{16} \, x^{4} + \frac{3851307}{64} \, x^{3} + \frac{11140101}{128} \, x^{2} + \frac{35458963}{256} \, x - \frac{14235529}{512 \,{\left (2 \, x - 1\right )}} + \frac{12386759}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="maxima")

[Out]

18225/28*x^7 + 37665/8*x^6 + 1295919/80*x^5 + 575775/16*x^4 + 3851307/64*x^3 + 1
1140101/128*x^2 + 35458963/256*x - 14235529/512/(2*x - 1) + 12386759/128*log(2*x
- 1)

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Fricas [A]  time = 0.224704, size = 84, normalized size = 1.22 \[ \frac{23328000 \, x^{8} + 157075200 \, x^{7} + 496202112 \, x^{6} + 999450144 \, x^{5} + 1511863920 \, x^{4} + 2040862320 \, x^{3} + 3404640680 \, x^{2} + 1734146260 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2482127410 \, x - 498243515}{17920 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="fricas")

[Out]

1/17920*(23328000*x^8 + 157075200*x^7 + 496202112*x^6 + 999450144*x^5 + 15118639
20*x^4 + 2040862320*x^3 + 3404640680*x^2 + 1734146260*(2*x - 1)*log(2*x - 1) - 2
482127410*x - 498243515)/(2*x - 1)

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Sympy [A]  time = 0.254365, size = 61, normalized size = 0.88 \[ \frac{18225 x^{7}}{28} + \frac{37665 x^{6}}{8} + \frac{1295919 x^{5}}{80} + \frac{575775 x^{4}}{16} + \frac{3851307 x^{3}}{64} + \frac{11140101 x^{2}}{128} + \frac{35458963 x}{256} + \frac{12386759 \log{\left (2 x - 1 \right )}}{128} - \frac{14235529}{1024 x - 512} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**6*(3+5*x)**2/(1-2*x)**2,x)

[Out]

18225*x**7/28 + 37665*x**6/8 + 1295919*x**5/80 + 575775*x**4/16 + 3851307*x**3/6
4 + 11140101*x**2/128 + 35458963*x/256 + 12386759*log(2*x - 1)/128 - 14235529/(1
024*x - 512)

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GIAC/XCAS [A]  time = 0.210623, size = 126, normalized size = 1.83 \[ \frac{1}{17920} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{1956150}{2 \, x - 1} + \frac{18894708}{{\left (2 \, x - 1\right )}^{2}} + \frac{108624915}{{\left (2 \, x - 1\right )}^{3}} + \frac{416281950}{{\left (2 \, x - 1\right )}^{4}} + \frac{1148518350}{{\left (2 \, x - 1\right )}^{5}} + \frac{2640379700}{{\left (2 \, x - 1\right )}^{6}} + 91125\right )} - \frac{14235529}{512 \,{\left (2 \, x - 1\right )}} - \frac{12386759}{128} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="giac")

[Out]

1/17920*(2*x - 1)^7*(1956150/(2*x - 1) + 18894708/(2*x - 1)^2 + 108624915/(2*x -
1)^3 + 416281950/(2*x - 1)^4 + 1148518350/(2*x - 1)^5 + 2640379700/(2*x - 1)^6
+ 91125) - 14235529/512/(2*x - 1) - 12386759/128*ln(1/2*abs(2*x - 1)/(2*x - 1)^2
)