3.1666 \(\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=86 \[ \frac{2672}{2033647 (1-2 x)}+\frac{39393}{16807 (3 x+2)}+\frac{8}{26411 (1-2 x)^2}+\frac{1107}{4802 (3 x+2)^2}+\frac{9}{343 (3 x+2)^3}-\frac{267760 \log (1-2 x)}{156590819}-\frac{1380915 \log (3 x+2)}{117649}+\frac{15625 \log (5 x+3)}{1331} \]

[Out]

8/(26411*(1 - 2*x)^2) + 2672/(2033647*(1 - 2*x)) + 9/(343*(2 + 3*x)^3) + 1107/(4
802*(2 + 3*x)^2) + 39393/(16807*(2 + 3*x)) - (267760*Log[1 - 2*x])/156590819 - (
1380915*Log[2 + 3*x])/117649 + (15625*Log[3 + 5*x])/1331

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Rubi [A]  time = 0.10132, antiderivative size = 86, 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 \[ \frac{2672}{2033647 (1-2 x)}+\frac{39393}{16807 (3 x+2)}+\frac{8}{26411 (1-2 x)^2}+\frac{1107}{4802 (3 x+2)^2}+\frac{9}{343 (3 x+2)^3}-\frac{267760 \log (1-2 x)}{156590819}-\frac{1380915 \log (3 x+2)}{117649}+\frac{15625 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

[In]  Int[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

8/(26411*(1 - 2*x)^2) + 2672/(2033647*(1 - 2*x)) + 9/(343*(2 + 3*x)^3) + 1107/(4
802*(2 + 3*x)^2) + 39393/(16807*(2 + 3*x)) - (267760*Log[1 - 2*x])/156590819 - (
1380915*Log[2 + 3*x])/117649 + (15625*Log[3 + 5*x])/1331

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Rubi in Sympy [A]  time = 12.8778, size = 73, normalized size = 0.85 \[ - \frac{267760 \log{\left (- 2 x + 1 \right )}}{156590819} - \frac{1380915 \log{\left (3 x + 2 \right )}}{117649} + \frac{15625 \log{\left (5 x + 3 \right )}}{1331} + \frac{39393}{16807 \left (3 x + 2\right )} + \frac{1107}{4802 \left (3 x + 2\right )^{2}} + \frac{9}{343 \left (3 x + 2\right )^{3}} + \frac{2672}{2033647 \left (- 2 x + 1\right )} + \frac{8}{26411 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1-2*x)**3/(2+3*x)**4/(3+5*x),x)

[Out]

-267760*log(-2*x + 1)/156590819 - 1380915*log(3*x + 2)/117649 + 15625*log(5*x +
3)/1331 + 39393/(16807*(3*x + 2)) + 1107/(4802*(3*x + 2)**2) + 9/(343*(3*x + 2)*
*3) + 2672/(2033647*(-2*x + 1)) + 8/(26411*(-2*x + 1)**2)

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Mathematica [A]  time = 0.153722, size = 69, normalized size = 0.8 \[ \frac{5 \left (\frac{77 \left (342903240 x^4+125249220 x^3-222614730 x^2-43096225 x+40167012\right )}{5 (1-2 x)^2 (3 x+2)^3}-107104 \log (5-10 x)-735199146 \log (5 (3 x+2))[phone] \log (5 x+3)\right )}{313181638} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

(5*((77*(40167012 - 43096225*x - 222614730*x^2 + 125249220*x^3 + 342903240*x^4))
/(5*(1 - 2*x)^2*(2 + 3*x)^3) - 107104*Log[5 - 10*x] - 735199146*Log[5*(2 + 3*x)]
+ 735306250*Log[3 + 5*x]))/313181638

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Maple [A]  time = 0.017, size = 71, normalized size = 0.8 \[{\frac{15625\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{9}{343\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1107}{4802\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{39393}{33614+50421\,x}}-{\frac{1380915\,\ln \left ( 2+3\,x \right ) }{117649}}+{\frac{8}{26411\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{2672}{-2033647+4067294\,x}}-{\frac{267760\,\ln \left ( -1+2\,x \right ) }{156590819}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^3/(2+3*x)^4/(3+5*x),x)

[Out]

15625/1331*ln(3+5*x)+9/343/(2+3*x)^3+1107/4802/(2+3*x)^2+39393/16807/(2+3*x)-138
0915/117649*ln(2+3*x)+8/26411/(-1+2*x)^2-2672/2033647/(-1+2*x)-267760/156590819*
ln(-1+2*x)

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Maxima [A]  time = 1.32716, size = 100, normalized size = 1.16 \[ \frac{342903240 \, x^{4} + 125249220 \, x^{3} - 222614730 \, x^{2} - 43096225 \, x + 40167012}{4067294 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac{15625}{1331} \, \log \left (5 \, x + 3\right ) - \frac{1380915}{117649} \, \log \left (3 \, x + 2\right ) - \frac{267760}{156590819} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^3),x, algorithm="maxima")

[Out]

1/4067294*(342903240*x^4 + 125249220*x^3 - 222614730*x^2 - 43096225*x + 40167012
)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8) + 15625/1331*log(5*x + 3) - 13
80915/117649*log(3*x + 2) - 267760/156590819*log(2*x - 1)

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Fricas [A]  time = 0.224291, size = 200, normalized size = 2.33 \[ \frac{26403549480 \, x^{4} + 9644189940 \, x^{3} - 17141334210 \, x^{2} + 3676531250 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 3675995730 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 535520 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 3318409325 \, x + 3092859924}{313181638 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^3),x, algorithm="fricas")

[Out]

1/313181638*(26403549480*x^4 + 9644189940*x^3 - 17141334210*x^2 + 3676531250*(10
8*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(5*x + 3) - 3675995730*(108*x^5
+ 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) - 535520*(108*x^5 + 108*x^4
- 45*x^3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 3318409325*x + 3092859924)/(108*x^5
+ 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)

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Sympy [A]  time = 0.663606, size = 75, normalized size = 0.87 \[ \frac{342903240 x^{4} + 125249220 x^{3} - 222614730 x^{2} - 43096225 x + 40167012}{439267752 x^{5} + 439267752 x^{4} - 183028230 x^{3} - 235903052 x^{2} + 16269176 x + 32538352} - \frac{267760 \log{\left (x - \frac{1}{2} \right )}}{156590819} + \frac{15625 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{1380915 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-2*x)**3/(2+3*x)**4/(3+5*x),x)

[Out]

(342903240*x**4 + 125249220*x**3 - 222614730*x**2 - 43096225*x + 40167012)/(4392
67752*x**5 + 439267752*x**4 - 183028230*x**3 - 235903052*x**2 + 16269176*x + 325
38352) - 267760*log(x - 1/2)/156590819 + 15625*log(x + 3/5)/1331 - 1380915*log(x
+ 2/3)/117649

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GIAC/XCAS [A]  time = 0.215782, size = 86, normalized size = 1. \[ \frac{342903240 \, x^{4} + 125249220 \, x^{3} - 222614730 \, x^{2} - 43096225 \, x + 40167012}{4067294 \,{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{15625}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1380915}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{267760}{156590819} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^3),x, algorithm="giac")

[Out]

1/4067294*(342903240*x^4 + 125249220*x^3 - 222614730*x^2 - 43096225*x + 40167012
)/((3*x + 2)^3*(2*x - 1)^2) + 15625/1331*ln(abs(5*x + 3)) - 1380915/117649*ln(ab
s(3*x + 2)) - 267760/156590819*ln(abs(2*x - 1))