3.1466 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^8} \, dx\)

Optimal. Leaf size=98 \[ -\frac{10648}{823543 (3 x+2)}-\frac{2662}{117649 (3 x+2)^2}-\frac{2662}{50421 (3 x+2)^3}-\frac{1331}{9604 (3 x+2)^4}+\frac{3469}{46305 (3 x+2)^5}-\frac{103}{7938 (3 x+2)^6}+\frac{1}{1323 (3 x+2)^7}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (3 x+2)}{5764801} \]

[Out]

1/(1323*(2 + 3*x)^7) - 103/(7938*(2 + 3*x)^6) + 3469/(46305*(2 + 3*x)^5) - 1331/
(9604*(2 + 3*x)^4) - 2662/(50421*(2 + 3*x)^3) - 2662/(117649*(2 + 3*x)^2) - 1064
8/(823543*(2 + 3*x)) - (21296*Log[1 - 2*x])/5764801 + (21296*Log[2 + 3*x])/57648
01

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Rubi [A]  time = 0.0963738, antiderivative size = 98, 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 \[ -\frac{10648}{823543 (3 x+2)}-\frac{2662}{117649 (3 x+2)^2}-\frac{2662}{50421 (3 x+2)^3}-\frac{1331}{9604 (3 x+2)^4}+\frac{3469}{46305 (3 x+2)^5}-\frac{103}{7938 (3 x+2)^6}+\frac{1}{1323 (3 x+2)^7}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (3 x+2)}{5764801} \]

Antiderivative was successfully verified.

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

[Out]

1/(1323*(2 + 3*x)^7) - 103/(7938*(2 + 3*x)^6) + 3469/(46305*(2 + 3*x)^5) - 1331/
(9604*(2 + 3*x)^4) - 2662/(50421*(2 + 3*x)^3) - 2662/(117649*(2 + 3*x)^2) - 1064
8/(823543*(2 + 3*x)) - (21296*Log[1 - 2*x])/5764801 + (21296*Log[2 + 3*x])/57648
01

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Rubi in Sympy [A]  time = 14.1837, size = 87, normalized size = 0.89 \[ - \frac{21296 \log{\left (- 2 x + 1 \right )}}{5764801} + \frac{21296 \log{\left (3 x + 2 \right )}}{5764801} - \frac{10648}{823543 \left (3 x + 2\right )} - \frac{2662}{117649 \left (3 x + 2\right )^{2}} - \frac{2662}{50421 \left (3 x + 2\right )^{3}} - \frac{1331}{9604 \left (3 x + 2\right )^{4}} + \frac{3469}{46305 \left (3 x + 2\right )^{5}} - \frac{103}{7938 \left (3 x + 2\right )^{6}} + \frac{1}{1323 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-21296*log(-2*x + 1)/5764801 + 21296*log(3*x + 2)/5764801 - 10648/(823543*(3*x +
2)) - 2662/(117649*(3*x + 2)**2) - 2662/(50421*(3*x + 2)**3) - 1331/(9604*(3*x
+ 2)**4) + 3469/(46305*(3*x + 2)**5) - 103/(7938*(3*x + 2)**6) + 1/(1323*(3*x +
2)**7)

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Mathematica [A]  time = 0.0899703, size = 62, normalized size = 0.63 \[ \frac{4 \left (-\frac{7 \left (12575075040 x^6+57635760600 x^5+113990726520 x^4+127327486275 x^3+83293304778 x^2+29451465714 x+4309941128\right )}{16 (3 x+2)^7}-2156220 \log (1-2 x)+2156220 \log (6 x+4)\right )}{2334744405} \]

Antiderivative was successfully verified.

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

[Out]

(4*((-7*(4309941128 + 29451465714*x + 83293304778*x^2 + 127327486275*x^3 + 11399
0726520*x^4 + 57635760600*x^5 + 12575075040*x^6))/(16*(2 + 3*x)^7) - 2156220*Log
[1 - 2*x] + 2156220*Log[4 + 6*x]))/2334744405

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Maple [A]  time = 0.013, size = 81, normalized size = 0.8 \[{\frac{1}{1323\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{103}{7938\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{3469}{46305\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1331}{9604\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2662}{50421\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2662}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{10648}{1647086+2470629\,x}}+{\frac{21296\,\ln \left ( 2+3\,x \right ) }{5764801}}-{\frac{21296\,\ln \left ( -1+2\,x \right ) }{5764801}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1323/(2+3*x)^7-103/7938/(2+3*x)^6+3469/46305/(2+3*x)^5-1331/9604/(2+3*x)^4-266
2/50421/(2+3*x)^3-2662/117649/(2+3*x)^2-10648/823543/(2+3*x)+21296/5764801*ln(2+
3*x)-21296/5764801*ln(-1+2*x)

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Maxima [A]  time = 1.3556, size = 116, normalized size = 1.18 \[ -\frac{12575075040 \, x^{6} + 57635760600 \, x^{5} + 113990726520 \, x^{4} + 127327486275 \, x^{3} + 83293304778 \, x^{2} + 29451465714 \, x + 4309941128}{1334139660 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{21296}{5764801} \, \log \left (3 \, x + 2\right ) - \frac{21296}{5764801} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1334139660*(12575075040*x^6 + 57635760600*x^5 + 113990726520*x^4 + 1273274862
75*x^3 + 83293304778*x^2 + 29451465714*x + 4309941128)/(2187*x^7 + 10206*x^6 + 2
0412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128) + 21296/5764801*log(
3*x + 2) - 21296/5764801*log(2*x - 1)

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Fricas [A]  time = 0.213773, size = 209, normalized size = 2.13 \[ -\frac{88025525280 \, x^{6} + 403450324200 \, x^{5} + 797935085640 \, x^{4} + 891292403925 \, x^{3} + 583053133446 \, x^{2} - 34499520 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 34499520 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (2 \, x - 1\right ) + 206160259998 \, x + 30169587896}{9338977620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/9338977620*(88025525280*x^6 + 403450324200*x^5 + 797935085640*x^4 + 891292403
925*x^3 + 583053133446*x^2 - 34499520*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*
x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 34499520*(2187*x^7 + 1
0206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(2*x
- 1) + 206160259998*x + 30169587896)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x
^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Sympy [A]  time = 0.639227, size = 85, normalized size = 0.87 \[ - \frac{12575075040 x^{6} + 57635760600 x^{5} + 113990726520 x^{4} + 127327486275 x^{3} + 83293304778 x^{2} + 29451465714 x + 4309941128}{2917763436420 x^{7} + 13616229369960 x^{6} + 27232458739920 x^{5} + 30258287488800 x^{4} + 20172191659200 x^{3} + 8068876663680 x^{2} + 1793083703040 x + 170769876480} - \frac{21296 \log{\left (x - \frac{1}{2} \right )}}{5764801} + \frac{21296 \log{\left (x + \frac{2}{3} \right )}}{5764801} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(12575075040*x**6 + 57635760600*x**5 + 113990726520*x**4 + 127327486275*x**3 +
83293304778*x**2 + 29451465714*x + 4309941128)/(2917763436420*x**7 + 13616229369
960*x**6 + 27232458739920*x**5 + 30258287488800*x**4 + 20172191659200*x**3 + 806
8876663680*x**2 + 1793083703040*x + 170769876480) - 21296*log(x - 1/2)/5764801 +
21296*log(x + 2/3)/5764801

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GIAC/XCAS [A]  time = 0.205144, size = 78, normalized size = 0.8 \[ -\frac{12575075040 \, x^{6} + 57635760600 \, x^{5} + 113990726520 \, x^{4} + 127327486275 \, x^{3} + 83293304778 \, x^{2} + 29451465714 \, x + 4309941128}{1334139660 \,{\left (3 \, x + 2\right )}^{7}} + \frac{21296}{5764801} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{21296}{5764801} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1334139660*(12575075040*x^6 + 57635760600*x^5 + 113990726520*x^4 + 1273274862
75*x^3 + 83293304778*x^2 + 29451465714*x + 4309941128)/(3*x + 2)^7 + 21296/57648
01*ln(abs(3*x + 2)) - 21296/5764801*ln(abs(2*x - 1))