3.1653 \(\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^5} \, dx\)

Optimal. Leaf size=87 \[ \frac{14520}{117649 (1-2 x)}-\frac{7755}{117649 (3 x+2)}+\frac{1331}{16807 (1-2 x)^2}+\frac{1023}{33614 (3 x+2)^2}-\frac{11}{2401 (3 x+2)^3}+\frac{1}{4116 (3 x+2)^4}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (3 x+2)}{823543} \]

[Out]

1331/(16807*(1 - 2*x)^2) + 14520/(117649*(1 - 2*x)) + 1/(4116*(2 + 3*x)^4) - 11/
(2401*(2 + 3*x)^3) + 1023/(33614*(2 + 3*x)^2) - 7755/(117649*(2 + 3*x)) - (59070
*Log[1 - 2*x])/823543 + (59070*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.10478, antiderivative size = 87, 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 \[ \frac{14520}{117649 (1-2 x)}-\frac{7755}{117649 (3 x+2)}+\frac{1331}{16807 (1-2 x)^2}+\frac{1023}{33614 (3 x+2)^2}-\frac{11}{2401 (3 x+2)^3}+\frac{1}{4116 (3 x+2)^4}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

1331/(16807*(1 - 2*x)^2) + 14520/(117649*(1 - 2*x)) + 1/(4116*(2 + 3*x)^4) - 11/
(2401*(2 + 3*x)^3) + 1023/(33614*(2 + 3*x)^2) - 7755/(117649*(2 + 3*x)) - (59070
*Log[1 - 2*x])/823543 + (59070*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 13.0343, size = 73, normalized size = 0.84 \[ - \frac{59070 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{59070 \log{\left (3 x + 2 \right )}}{823543} - \frac{7755}{117649 \left (3 x + 2\right )} + \frac{1023}{33614 \left (3 x + 2\right )^{2}} - \frac{11}{2401 \left (3 x + 2\right )^{3}} + \frac{1}{4116 \left (3 x + 2\right )^{4}} + \frac{14520}{117649 \left (- 2 x + 1\right )} + \frac{1331}{16807 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-59070*log(-2*x + 1)/823543 + 59070*log(3*x + 2)/823543 - 7755/(117649*(3*x + 2)
) + 1023/(33614*(3*x + 2)**2) - 11/(2401*(3*x + 2)**3) + 1/(4116*(3*x + 2)**4) +
14520/(117649*(-2*x + 1)) + 1331/(16807*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0932203, size = 64, normalized size = 0.74 \[ \frac{-\frac{7 \left (38277360 x^5+60605820 x^4+8860500 x^3-32767930 x^2-21371408 x-3991495\right )}{4 (1-2 x)^2 (3 x+2)^4}-177210 \log (1-2 x)+177210 \log (6 x+4)}{2470629} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(-3991495 - 21371408*x - 32767930*x^2 + 8860500*x^3 + 60605820*x^4 + 382773
60*x^5))/(4*(1 - 2*x)^2*(2 + 3*x)^4) - 177210*Log[1 - 2*x] + 177210*Log[4 + 6*x]
)/2470629

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Maple [A]  time = 0.016, size = 72, normalized size = 0.8 \[{\frac{1}{4116\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11}{2401\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1023}{33614\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{7755}{235298+352947\,x}}+{\frac{59070\,\ln \left ( 2+3\,x \right ) }{823543}}+{\frac{1331}{16807\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{14520}{-117649+235298\,x}}-{\frac{59070\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4116/(2+3*x)^4-11/2401/(2+3*x)^3+1023/33614/(2+3*x)^2-7755/117649/(2+3*x)+5907
0/823543*ln(2+3*x)+1331/16807/(-1+2*x)^2-14520/117649/(-1+2*x)-59070/823543*ln(-
1+2*x)

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Maxima [A]  time = 1.35296, size = 103, normalized size = 1.18 \[ -\frac{38277360 \, x^{5} + 60605820 \, x^{4} + 8860500 \, x^{3} - 32767930 \, x^{2} - 21371408 \, x - 3991495}{1411788 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} + \frac{59070}{823543} \, \log \left (3 \, x + 2\right ) - \frac{59070}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1411788*(38277360*x^5 + 60605820*x^4 + 8860500*x^3 - 32767930*x^2 - 21371408*
x - 3991495)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16) + 5907
0/823543*log(3*x + 2) - 59070/823543*log(2*x - 1)

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Fricas [A]  time = 0.214253, size = 182, normalized size = 2.09 \[ -\frac{267941520 \, x^{5} + 424240740 \, x^{4} + 62023500 \, x^{3} - 229375510 \, x^{2} - 708840 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 708840 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (2 \, x - 1\right ) - 149599856 \, x - 27940465}{9882516 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/9882516*(267941520*x^5 + 424240740*x^4 + 62023500*x^3 - 229375510*x^2 - 70884
0*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(3*x + 2) + 70
8840*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(2*x - 1) -
149599856*x - 27940465)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x
+ 16)

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Sympy [A]  time = 0.626715, size = 75, normalized size = 0.86 \[ - \frac{38277360 x^{5} + 60605820 x^{4} + 8860500 x^{3} - 32767930 x^{2} - 21371408 x - 3991495}{457419312 x^{6} + 762365520 x^{5} + 114354828 x^{4} - 372712032 x^{3} - 146825952 x^{2} + 45177216 x + 22588608} - \frac{59070 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{59070 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(38277360*x**5 + 60605820*x**4 + 8860500*x**3 - 32767930*x**2 - 21371408*x - 39
91495)/(457419312*x**6 + 762365520*x**5 + 114354828*x**4 - 372712032*x**3 - 1468
25952*x**2 + 45177216*x + 22588608) - 59070*log(x - 1/2)/823543 + 59070*log(x +
2/3)/823543

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GIAC/XCAS [A]  time = 0.212454, size = 105, normalized size = 1.21 \[ -\frac{7755}{117649 \,{\left (3 \, x + 2\right )}} + \frac{4356 \,{\left (\frac{217}{3 \, x + 2} - 51\right )}}{823543 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} + \frac{1023}{33614 \,{\left (3 \, x + 2\right )}^{2}} - \frac{11}{2401 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{4116 \,{\left (3 \, x + 2\right )}^{4}} - \frac{59070}{823543} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7755/117649/(3*x + 2) + 4356/823543*(217/(3*x + 2) - 51)/(7/(3*x + 2) - 2)^2 +
1023/33614/(3*x + 2)^2 - 11/2401/(3*x + 2)^3 + 1/4116/(3*x + 2)^4 - 59070/823543
*ln(abs(-7/(3*x + 2) + 2))