3.1554 \(\int \frac{(2+3 x)^8 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=90 \[ \frac{164025 x^{10}}{8}+\frac{370575 x^9}{2}+\frac{101721015 x^8}{128}+\frac{242570133 x^7}{112}+\frac{544462047 x^6}{128}+\frac{260574273 x^5}{40}+\frac{8502681987 x^4}{1024}+\frac{2416569641 x^3}{256}+\frac{21573106793 x^2}{2048}+\frac{7277894263 x}{512}+\frac{7672950131}{4096 (1-2 x)}+\frac{36770371407 \log (1-2 x)}{4096} \]

[Out]

7672950131/(4096*(1 - 2*x)) + (7277894263*x)/512 + (21573106793*x^2)/2048 + (241
6569641*x^3)/256 + (8502681987*x^4)/1024 + (260574273*x^5)/40 + (544462047*x^6)/
128 + (242570133*x^7)/112 + (101721015*x^8)/128 + (370575*x^9)/2 + (164025*x^10)
/8 + (36770371407*Log[1 - 2*x])/4096

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Rubi [A]  time = 0.116036, antiderivative size = 90, 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 \[ \frac{164025 x^{10}}{8}+\frac{370575 x^9}{2}+\frac{101721015 x^8}{128}+\frac{242570133 x^7}{112}+\frac{544462047 x^6}{128}+\frac{260574273 x^5}{40}+\frac{8502681987 x^4}{1024}+\frac{2416569641 x^3}{256}+\frac{21573106793 x^2}{2048}+\frac{7277894263 x}{512}+\frac{7672950131}{4096 (1-2 x)}+\frac{36770371407 \log (1-2 x)}{4096} \]

Antiderivative was successfully verified.

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

[Out]

7672950131/(4096*(1 - 2*x)) + (7277894263*x)/512 + (21573106793*x^2)/2048 + (241
6569641*x^3)/256 + (8502681987*x^4)/1024 + (260574273*x^5)/40 + (544462047*x^6)/
128 + (242570133*x^7)/112 + (101721015*x^8)/128 + (370575*x^9)/2 + (164025*x^10)
/8 + (36770371407*Log[1 - 2*x])/4096

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{164025 x^{10}}{8} + \frac{370575 x^{9}}{2} + \frac{101721015 x^{8}}{128} + \frac{242570133 x^{7}}{112} + \frac{544462047 x^{6}}{128} + \frac{260574273 x^{5}}{40} + \frac{8502681987 x^{4}}{1024} + \frac{2416569641 x^{3}}{256} + \frac{36770371407 \log{\left (- 2 x + 1 \right )}}{4096} + \int \frac{7277894263}{512}\, dx + \frac{21573106793 \int x\, dx}{1024} + \frac{7672950131}{4096 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

164025*x**10/8 + 370575*x**9/2 + 101721015*x**8/128 + 242570133*x**7/112 + 54446
2047*x**6/128 + 260574273*x**5/40 + 8502681987*x**4/1024 + 2416569641*x**3/256 +
36770371407*log(-2*x + 1)/4096 + Integral(7277894263/512, x) + 21573106793*Inte
gral(x, x)/1024 + 7672950131/(4096*(-2*x + 1))

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Mathematica [A]  time = 0.0320927, size = 79, normalized size = 0.88 \[ \frac{47029248000 x^{11}[phone] x^{10}[phone] x^9+4056416029440 x^8+7272841720320 x^7+10063991169792 x^6+11574822095424 x^5+12129460157920 x^4+13335647616480 x^3+20524026494160 x^2-43208575854086 x+10295703993960 (2 x-1) \log (1-2 x)[phone]}{1146880 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(11304620315803 - 43208575854086*x + 20524026494160*x^2 + 13335647616480*x^3 + 1
2129460157920*x^4 + 11574822095424*x^5 + 10063991169792*x^6 + 7272841720320*x^7
+ 4056416029440*x^8 + 1610338060800*x^9 + 401490432000*x^10 + 47029248000*x^11 +
10295703993960*(-1 + 2*x)*Log[1 - 2*x])/(1146880*(-1 + 2*x))

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Maple [A]  time = 0.012, size = 67, normalized size = 0.7 \[{\frac{164025\,{x}^{10}}{8}}+{\frac{370575\,{x}^{9}}{2}}+{\frac{101721015\,{x}^{8}}{128}}+{\frac{242570133\,{x}^{7}}{112}}+{\frac{544462047\,{x}^{6}}{128}}+{\frac{260574273\,{x}^{5}}{40}}+{\frac{8502681987\,{x}^{4}}{1024}}+{\frac{2416569641\,{x}^{3}}{256}}+{\frac{21573106793\,{x}^{2}}{2048}}+{\frac{7277894263\,x}{512}}-{\frac{7672950131}{-4096+8192\,x}}+{\frac{36770371407\,\ln \left ( -1+2\,x \right ) }{4096}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

164025/8*x^10+370575/2*x^9+101721015/128*x^8+242570133/112*x^7+544462047/128*x^6
[phone]/40*x^5+8502681987/1024*x^4+2416569641/256*x^3+21573106793/2048*x^2+72
77894263/512*x-7672950131/4096/(-1+2*x)[phone]/4096*ln(-1+2*x)

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Maxima [A]  time = 1.34936, size = 89, normalized size = 0.99 \[ \frac{164025}{8} \, x^{10} + \frac{370575}{2} \, x^{9} + \frac{101721015}{128} \, x^{8} + \frac{242570133}{112} \, x^{7} + \frac{544462047}{128} \, x^{6} + \frac{260574273}{40} \, x^{5} + \frac{8502681987}{1024} \, x^{4} + \frac{2416569641}{256} \, x^{3} + \frac{21573106793}{2048} \, x^{2} + \frac{7277894263}{512} \, x - \frac{7672950131}{4096 \,{\left (2 \, x - 1\right )}} + \frac{36770371407}{4096} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

164025/8*x^10 + 370575/2*x^9 + 101721015/128*x^8 + 242570133/112*x^7 + 544462047
/128*x^6 + 260574273/40*x^5 + 8502681987/1024*x^4 + 2416569641/256*x^3 + 2157310
6793/2048*x^2 + 7277894263/512*x - 7672950131/4096/(2*x - 1) + 36770371407/4096*
log(2*x - 1)

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Fricas [A]  time = 0.212495, size = 104, normalized size = 1.16 \[ \frac{5878656000 \, x^{11} + 50186304000 \, x^{10} + 201292257600 \, x^{9} + 507052003680 \, x^{8} + 909105215040 \, x^{7} + 1257998896224 \, x^{6} + 1446852761928 \, x^{5} + 1516182519740 \, x^{4} + 1666955952060 \, x^{3} + 2565503311770 \, x^{2} + 1286962999245 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2037810393640 \, x - 268553254585}{143360 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/143360*(5878656000*x^11 + 50186304000*x^10 + 201292257600*x^9 + 507052003680*x
^8 + 909105215040*x^7 + 1257998896224*x^6 + 1446852761928*x^5 + 1516182519740*x^
4 + 1666955952060*x^3 + 2565503311770*x^2 + 1286962999245*(2*x - 1)*log(2*x - 1)
- 2037810393640*x - 268553254585)/(2*x - 1)

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Sympy [A]  time = 0.293069, size = 82, normalized size = 0.91 \[ \frac{164025 x^{10}}{8} + \frac{370575 x^{9}}{2} + \frac{101721015 x^{8}}{128} + \frac{242570133 x^{7}}{112} + \frac{544462047 x^{6}}{128} + \frac{260574273 x^{5}}{40} + \frac{8502681987 x^{4}}{1024} + \frac{2416569641 x^{3}}{256} + \frac{21573106793 x^{2}}{2048} + \frac{7277894263 x}{512} + \frac{36770371407 \log{\left (2 x - 1 \right )}}{4096} - \frac{7672950131}{8192 x - 4096} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

164025*x**10/8 + 370575*x**9/2 + 101721015*x**8/128 + 242570133*x**7/112 + 54446
2047*x**6/128 + 260574273*x**5/40 + 8502681987*x**4/1024 + 2416569641*x**3/256 +
21573106793*x**2/2048 + 7277894263*x/512 + 36770371407*log(2*x - 1)/4096 - 7672
950131/(8192*x - 4096)

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GIAC/XCAS [A]  time = 0.213203, size = 162, normalized size = 1.8 \[ \frac{1}{1146880} \,{\left (2 \, x - 1\right )}^{10}{\left (\frac{644679000}{2 \, x - 1} + \frac{8328989025}{{\left (2 \, x - 1\right )}^{2}} + \frac{65584698840}{{\left (2 \, x - 1\right )}^{3}} + \frac{351436586760}{{\left (2 \, x - 1\right )}^{4}} + \frac{1355796026928}{{\left (2 \, x - 1\right )}^{5}} + \frac{3891461518980}{{\left (2 \, x - 1\right )}^{6}} + \frac{8509458050800}{{\left (2 \, x - 1\right )}^{7}} + \frac{14652493526860}{{\left (2 \, x - 1\right )}^{8}} + \frac{22425306482040}{{\left (2 \, x - 1\right )}^{9}} + 22963500\right )} - \frac{7672950131}{4096 \,{\left (2 \, x - 1\right )}} - \frac{36770371407}{4096} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1146880*(2*x - 1)^10*(644679000/(2*x - 1) + 8328989025/(2*x - 1)^2 + 655846988
40/(2*x - 1)^3 + 351436586760/(2*x - 1)^4 + 1355796026928/(2*x - 1)^5 + 38914615
18980/(2*x - 1)^6 + 8509458050800/(2*x - 1)^7 + 14652493526860/(2*x - 1)^8 + 224
25306482040/(2*x - 1)^9 + 22963500) - 7672950131/4096/(2*x - 1) - 36770371407/40
96*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)