3.1521 \(\int \frac{(2+3 x)^8 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=76 \[ \frac{32805 x^8}{32}+\frac{56862 x^7}{7}+\frac{976617 x^6}{32}+\frac{5859459 x^5}{80}+\frac{32991057 x^4}{256}+\frac{5892813 x^3}{32}+\frac{122887143 x^2}{512}+\frac{91609881 x}{256}+\frac{63412811}{1024 (1-2 x)}+\frac{246239357 \log (1-2 x)}{1024} \]

[Out]

63412811/(1024*(1 - 2*x)) + (91609881*x)/256 + (122887143*x^2)/512 + (5892813*x^
3)/32 + (32991057*x^4)/256 + (5859459*x^5)/80 + (976617*x^6)/32 + (56862*x^7)/7
+ (32805*x^8)/32 + (246239357*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0900259, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{32805 x^8}{32}+\frac{56862 x^7}{7}+\frac{976617 x^6}{32}+\frac{5859459 x^5}{80}+\frac{32991057 x^4}{256}+\frac{5892813 x^3}{32}+\frac{122887143 x^2}{512}+\frac{91609881 x}{256}+\frac{63412811}{1024 (1-2 x)}+\frac{246239357 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

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

[Out]

63412811/(1024*(1 - 2*x)) + (91609881*x)/256 + (122887143*x^2)/512 + (5892813*x^
3)/32 + (32991057*x^4)/256 + (5859459*x^5)/80 + (976617*x^6)/32 + (56862*x^7)/7
+ (32805*x^8)/32 + (246239357*Log[1 - 2*x])/1024

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{32805 x^{8}}{32} + \frac{56862 x^{7}}{7} + \frac{976617 x^{6}}{32} + \frac{5859459 x^{5}}{80} + \frac{32991057 x^{4}}{256} + \frac{5892813 x^{3}}{32} + \frac{246239357 \log{\left (- 2 x + 1 \right )}}{1024} + \int \frac{91609881}{256}\, dx + \frac{122887143 \int x\, dx}{256} + \frac{63412811}{1024 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

32805*x**8/32 + 56862*x**7/7 + 976617*x**6/32 + 5859459*x**5/80 + 32991057*x**4/
256 + 5892813*x**3/32 + 246239357*log(-2*x + 1)/1024 + Integral(91609881/256, x)
+ 122887143*Integral(x, x)/256 + 63412811/(1024*(-2*x + 1))

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Mathematica [A]  time = 0.0269714, size = 69, normalized size = 0.91 \[ \frac{587865600 x^9+4364202240 x^8+15171909120 x^7+33250113792 x^6+52899666624 x^5+68649225120 x^4+84833995680 x^3+136389333360 x^2-259057842186 x+68947019960 (2 x-1) \log (1-2 x)[phone]}{286720 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(60471800653 - 259057842186*x + 136389333360*x^2 + 84833995680*x^3 + 68649225120
*x^4 + 52899666624*x^5 + 33250113792*x^6 + 15171909120*x^7 + 4364202240*x^8 + 58
7865600*x^9 + 68947019960*(-1 + 2*x)*Log[1 - 2*x])/(286720*(-1 + 2*x))

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Maple [A]  time = 0.01, size = 57, normalized size = 0.8 \[{\frac{32805\,{x}^{8}}{32}}+{\frac{56862\,{x}^{7}}{7}}+{\frac{976617\,{x}^{6}}{32}}+{\frac{5859459\,{x}^{5}}{80}}+{\frac{32991057\,{x}^{4}}{256}}+{\frac{5892813\,{x}^{3}}{32}}+{\frac{122887143\,{x}^{2}}{512}}+{\frac{91609881\,x}{256}}-{\frac{63412811}{-1024+2048\,x}}+{\frac{246239357\,\ln \left ( -1+2\,x \right ) }{1024}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

32805/32*x^8+56862/7*x^7+976617/32*x^6+5859459/80*x^5+32991057/256*x^4+5892813/3
2*x^3+122887143/512*x^2+91609881/256*x-63412811/1024/(-1+2*x)[phone]/1024*ln(
-1+2*x)

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Maxima [A]  time = 1.34686, size = 76, normalized size = 1. \[ \frac{32805}{32} \, x^{8} + \frac{56862}{7} \, x^{7} + \frac{976617}{32} \, x^{6} + \frac{5859459}{80} \, x^{5} + \frac{32991057}{256} \, x^{4} + \frac{5892813}{32} \, x^{3} + \frac{122887143}{512} \, x^{2} + \frac{91609881}{256} \, x - \frac{63412811}{1024 \,{\left (2 \, x - 1\right )}} + \frac{246239357}{1024} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

32805/32*x^8 + 56862/7*x^7 + 976617/32*x^6 + 5859459/80*x^5 + 32991057/256*x^4 +
5892813/32*x^3 + 122887143/512*x^2 + 91609881/256*x - 63412811/1024/(2*x - 1) +
246239357/1024*log(2*x - 1)

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Fricas [A]  time = 0.214907, size = 90, normalized size = 1.18 \[ \frac{73483200 \, x^{9} + 545525280 \, x^{8} + 1896488640 \, x^{7} + 4156264224 \, x^{6} + 6612458328 \, x^{5} + 8581153140 \, x^{4} + 10604249460 \, x^{3} + 17048666670 \, x^{2} + 8618377495 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 12825383340 \, x - 2219448385}{35840 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/35840*(73483200*x^9 + 545525280*x^8 + 1896488640*x^7 + 4156264224*x^6 + 661245
8328*x^5 + 8581153140*x^4 + 10604249460*x^3 + 17048666670*x^2 + 8618377495*(2*x
- 1)*log(2*x - 1) - 12825383340*x - 2219448385)/(2*x - 1)

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Sympy [A]  time = 0.25071, size = 68, normalized size = 0.89 \[ \frac{32805 x^{8}}{32} + \frac{56862 x^{7}}{7} + \frac{976617 x^{6}}{32} + \frac{5859459 x^{5}}{80} + \frac{32991057 x^{4}}{256} + \frac{5892813 x^{3}}{32} + \frac{122887143 x^{2}}{512} + \frac{91609881 x}{256} + \frac{246239357 \log{\left (2 x - 1 \right )}}{1024} - \frac{63412811}{2048 x - 1024} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

32805*x**8/32 + 56862*x**7/7 + 976617*x**6/32 + 5859459*x**5/80 + 32991057*x**4/
256 + 5892813*x**3/32 + 122887143*x**2/512 + 91609881*x/256 + 246239357*log(2*x
- 1)/1024 - 63412811/(2048*x - 1024)

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GIAC/XCAS [A]  time = 0.208937, size = 138, normalized size = 1.82 \[ \frac{3}{286720} \,{\left (2 \, x - 1\right )}^{8}{\left (\frac{9127080}{2 \, x - 1} + \frac{98748720}{{\left (2 \, x - 1\right )}^{2}} + \frac{641009376}{{\left (2 \, x - 1\right )}^{3}} + \frac{2786264460}{{\left (2 \, x - 1\right )}^{4}} + \frac{8611906800}{{\left (2 \, x - 1\right )}^{5}} + \frac{19962682320}{{\left (2 \, x - 1\right )}^{6}} + \frac{39661830880}{{\left (2 \, x - 1\right )}^{7}} + 382725\right )} - \frac{63412811}{1024 \,{\left (2 \, x - 1\right )}} - \frac{246239357}{1024} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/286720*(2*x - 1)^8*(9127080/(2*x - 1) + 98748720/(2*x - 1)^2 + 641009376/(2*x
- 1)^3 + 2786264460/(2*x - 1)^4 + 8611906800/(2*x - 1)^5 + 19962682320/(2*x - 1)
^6 + 39661830880/(2*x - 1)^7 + 382725) - 63412811/1024/(2*x - 1) - 246239357/102
4*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)