3.1537 \(\int \frac{(2+3 x)^8 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=81 \[ \frac{18225 x^9}{4}+\frac{1235655 x^8}{32}+\frac{17378631 x^7}{112}+396738 x^6+\frac{235268793 x^5}{320}+\frac{275757561 x^4}{256}+\frac{346239417 x^3}{256}+\frac{413355417 x^2}{256}+\frac{2330515357 x}{1024}+\frac{697540921}{2048 (1-2 x)}+\frac{1512848491 \log (1-2 x)}{1024} \]

[Out]

697540921/(2048*(1 - 2*x)) + (2330515357*x)/1024 + (413355417*x^2)/256 + (346239
417*x^3)/256 + (275757561*x^4)/256 + (235268793*x^5)/320 + 396738*x^6 + (1737863
1*x^7)/112 + (1235655*x^8)/32 + (18225*x^9)/4 + (1512848491*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.109027, antiderivative size = 81, 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 \[ \frac{18225 x^9}{4}+\frac{1235655 x^8}{32}+\frac{17378631 x^7}{112}+396738 x^6+\frac{235268793 x^5}{320}+\frac{275757561 x^4}{256}+\frac{346239417 x^3}{256}+\frac{413355417 x^2}{256}+\frac{2330515357 x}{1024}+\frac{697540921}{2048 (1-2 x)}+\frac{1512848491 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x)^2,x]

[Out]

697540921/(2048*(1 - 2*x)) + (2330515357*x)/1024 + (413355417*x^2)/256 + (346239
417*x^3)/256 + (275757561*x^4)/256 + (235268793*x^5)/320 + 396738*x^6 + (1737863
1*x^7)/112 + (1235655*x^8)/32 + (18225*x^9)/4 + (1512848491*Log[1 - 2*x])/1024

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{18225 x^{9}}{4} + \frac{1235655 x^{8}}{32} + \frac{17378631 x^{7}}{112} + 396738 x^{6} + \frac{235268793 x^{5}}{320} + \frac{275757561 x^{4}}{256} + \frac{346239417 x^{3}}{256} + \frac{1512848491 \log{\left (- 2 x + 1 \right )}}{1024} + \int \frac{2330515357}{1024}\, dx + \frac{413355417 \int x\, dx}{128} + \frac{697540921}{2048 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**8*(3+5*x)**2/(1-2*x)**2,x)

[Out]

18225*x**9/4 + 1235655*x**8/32 + 17378631*x**7/112 + 396738*x**6 + 235268793*x**
5/320 + 275757561*x**4/256 + 346239417*x**3/256 + 1512848491*log(-2*x + 1)/1024
+ Integral(2330515357/1024, x) + 413355417*Integral(x, x)/128 + 697540921/(2048*
(-2*x + 1))

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Mathematica [A]  time = 0.0384268, size = 74, normalized size = 0.91 \[ \frac{2612736000 x^{10}[phone] x^9+77907121920 x^8+183016143360 x^7+307848957696 x^6+406896098112 x^5+466727825760 x^4+538127987040 x^3+842130532880 x^2-1689637297718 x+423597577480 (2 x-1) \log (1-2 x)[phone]}{286720 (2 x-1)} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x)^2,x]

[Out]

(420890769939 - 1689637297718*x + 842130532880*x^2 + 538127987040*x^3 + 46672782
5760*x^4 + 406896098112*x^5 + 307848957696*x^6 + 183016143360*x^7 + 77907121920*
x^8 + 20836569600*x^9 + 2612736000*x^10 + 423597577480*(-1 + 2*x)*Log[1 - 2*x])/
(286720*(-1 + 2*x))

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Maple [A]  time = 0.01, size = 62, normalized size = 0.8 \[{\frac{18225\,{x}^{9}}{4}}+{\frac{1235655\,{x}^{8}}{32}}+{\frac{17378631\,{x}^{7}}{112}}+396738\,{x}^{6}+{\frac{235268793\,{x}^{5}}{320}}+{\frac{275757561\,{x}^{4}}{256}}+{\frac{346239417\,{x}^{3}}{256}}+{\frac{413355417\,{x}^{2}}{256}}+{\frac{2330515357\,x}{1024}}-{\frac{697540921}{-2048+4096\,x}}+{\frac{1512848491\,\ln \left ( -1+2\,x \right ) }{1024}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^8*(3+5*x)^2/(1-2*x)^2,x)

[Out]

18225/4*x^9+1235655/32*x^8+17378631/112*x^7+396738*x^6+235268793/320*x^5+2757575
61/256*x^4+346239417/256*x^3+413355417/256*x^2+2330515357/1024*x-697540921/2048/
(-1+2*x)[phone]/1024*ln(-1+2*x)

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Maxima [A]  time = 1.32686, size = 82, normalized size = 1.01 \[ \frac{18225}{4} \, x^{9} + \frac{1235655}{32} \, x^{8} + \frac{17378631}{112} \, x^{7} + 396738 \, x^{6} + \frac{235268793}{320} \, x^{5} + \frac{275757561}{256} \, x^{4} + \frac{346239417}{256} \, x^{3} + \frac{413355417}{256} \, x^{2} + \frac{2330515357}{1024} \, x - \frac{697540921}{2048 \,{\left (2 \, x - 1\right )}} + \frac{1512848491}{1024} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="maxima")

[Out]

18225/4*x^9 + 1235655/32*x^8 + 17378631/112*x^7 + 396738*x^6 + 235268793/320*x^5
+ 275757561/256*x^4 + 346239417/256*x^3 + 413355417/256*x^2 + 2330515357/1024*x
- 697540921/2048/(2*x - 1) + 1512848491/1024*log(2*x - 1)

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Fricas [A]  time = 0.216128, size = 97, normalized size = 1.2 \[ \frac{653184000 \, x^{10} + 5209142400 \, x^{9} + 19476780480 \, x^{8} + 45754035840 \, x^{7} + 76962239424 \, x^{6} + 101724024528 \, x^{5} + 116681956440 \, x^{4} + 134531996760 \, x^{3} + 210532633220 \, x^{2} + 105899394370 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 163136074990 \, x - 24413932235}{71680 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="fricas")

[Out]

1/71680*(653184000*x^10 + 5209142400*x^9 + 19476780480*x^8 + 45754035840*x^7 + 7
6962239424*x^6 + 101724024528*x^5 + 116681956440*x^4 + 134531996760*x^3 + 210532
633220*x^2 + 105899394370*(2*x - 1)*log(2*x - 1) - 163136074990*x - 24413932235)
/(2*x - 1)

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Sympy [A]  time = 0.271709, size = 73, normalized size = 0.9 \[ \frac{18225 x^{9}}{4} + \frac{1235655 x^{8}}{32} + \frac{17378631 x^{7}}{112} + 396738 x^{6} + \frac{235268793 x^{5}}{320} + \frac{275757561 x^{4}}{256} + \frac{346239417 x^{3}}{256} + \frac{413355417 x^{2}}{256} + \frac{2330515357 x}{1024} + \frac{1512848491 \log{\left (2 x - 1 \right )}}{1024} - \frac{697540921}{4096 x - 2048} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**8*(3+5*x)**2/(1-2*x)**2,x)

[Out]

18225*x**9/4 + 1235655*x**8/32 + 17378631*x**7/112 + 396738*x**6 + 235268793*x**
5/320 + 275757561*x**4/256 + 346239417*x**3/256 + 413355417*x**2/256 + 233051535
7*x/1024 + 1512848491*log(2*x - 1)/1024 - 697540921/(4096*x - 2048)

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GIAC/XCAS [A]  time = 0.208438, size = 150, normalized size = 1.85 \[ \frac{1}{286720} \,{\left (2 \, x - 1\right )}^{9}{\left (\frac{66211425}{2 \, x - 1} + \frac{785410020}{{\left (2 \, x - 1\right )}^{2}} + \frac{5635662480}{{\left (2 \, x - 1\right )}^{3}} + \frac{27294241464}{{\left (2 \, x - 1\right )}^{4}} + \frac{94415339340}{{\left (2 \, x - 1\right )}^{5}} + \frac{241909873800}{{\left (2 \, x - 1\right )}^{6}} + \frac{478116124080}{{\left (2 \, x - 1\right )}^{7}} + \frac{826787759420}{{\left (2 \, x - 1\right )}^{8}} + 2551500\right )} - \frac{697540921}{2048 \,{\left (2 \, x - 1\right )}} - \frac{1512848491}{1024} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="giac")

[Out]

1/286720*(2*x - 1)^9*(66211425/(2*x - 1) + 785410020/(2*x - 1)^2 + 5635662480/(2
*x - 1)^3 + 27294241464/(2*x - 1)^4 + 94415339340/(2*x - 1)^5 + 241909873800/(2*
x - 1)^6 + 478116124080/(2*x - 1)^7 + 826787759420/(2*x - 1)^8 + 2551500) - 6975
40921/2048/(2*x - 1) - 1512848491/1024*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)