3.1599 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx\)

Optimal. Leaf size=97 \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]

[Out]

64/(2033647*(1 - 2*x)) - 27/(196*(2 + 3*x)^4) - 666/(343*(2 + 3*x)^3) - 107109/(
4802*(2 + 3*x)^2) - 5050944/(16807*(2 + 3*x)) - 15625/(121*(3 + 5*x)) - (15040*L
og[1 - 2*x])/156590819 + (222359715*Log[2 + 3*x])/117649 - (2515625*Log[3 + 5*x]
)/1331

_______________________________________________________________________________________

Rubi [A]  time = 0.119111, antiderivative size = 97, 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 \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

64/(2033647*(1 - 2*x)) - 27/(196*(2 + 3*x)^4) - 666/(343*(2 + 3*x)^3) - 107109/(
4802*(2 + 3*x)^2) - 5050944/(16807*(2 + 3*x)) - 15625/(121*(3 + 5*x)) - (15040*L
og[1 - 2*x])/156590819 + (222359715*Log[2 + 3*x])/117649 - (2515625*Log[3 + 5*x]
)/1331

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 14.2273, size = 80, normalized size = 0.82 \[ - \frac{15040 \log{\left (- 2 x + 1 \right )}}{156590819} + \frac{222359715 \log{\left (3 x + 2 \right )}}{117649} - \frac{2515625 \log{\left (5 x + 3 \right )}}{1331} - \frac{15625}{121 \left (5 x + 3\right )} - \frac{5050944}{16807 \left (3 x + 2\right )} - \frac{107109}{4802 \left (3 x + 2\right )^{2}} - \frac{666}{343 \left (3 x + 2\right )^{3}} - \frac{27}{196 \left (3 x + 2\right )^{4}} + \frac{64}{2033647 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15040*log(-2*x + 1)/156590819 + 222359715*log(3*x + 2)/117649 - 2515625*log(5*x
+ 3)/1331 - 15625/(121*(5*x + 3)) - 5050944/(16807*(3*x + 2)) - 107109/(4802*(3
*x + 2)**2) - 666/(343*(3*x + 2)**3) - 27/(196*(3*x + 2)**4) + 64/(2033647*(-2*x
+ 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.162597, size = 75, normalized size = 0.77 \[ \frac{-\frac{77 \left (830228340600 x^5+1771154199360 x^4+1064845635750 x^3-132753874800 x^2-317609203475 x-77754195847\right )}{(3 x+2)^4 \left (10 x^2+x-3\right )}-60160 \log (3-6 x)[phone] \log (3 x+2)-1183843062500 \log (-3 (5 x+3))}{626363276} \]

Antiderivative was successfully verified.

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

[Out]

((-77*(-77754195847 - 317609203475*x - 132753874800*x^2 + 1064845635750*x^3 + 17
71154199360*x^4 + 830228340600*x^5))/((2 + 3*x)^4*(-3 + x + 10*x^2)) - 60160*Log
[3 - 6*x] + 1183843122660*Log[2 + 3*x] - 1183843062500*Log[-3*(3 + 5*x)])/626363
276

_______________________________________________________________________________________

Maple [A]  time = 0.02, size = 80, normalized size = 0.8 \[ -{\frac{15625}{363+605\,x}}-{\frac{2515625\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{27}{196\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{666}{343\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107109}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5050944}{33614+50421\,x}}+{\frac{222359715\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{64}{-2033647+4067294\,x}}-{\frac{15040\,\ln \left ( -1+2\,x \right ) }{156590819}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15625/121/(3+5*x)-2515625/1331*ln(3+5*x)-27/196/(2+3*x)^4-666/343/(2+3*x)^3-107
109/4802/(2+3*x)^2-5050944/16807/(2+3*x)[phone]/117649*ln(2+3*x)-64/2033647/(
-1+2*x)-15040/156590819*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34438, size = 113, normalized size = 1.16 \[ -\frac{830228340600 \, x^{5} + 1771154199360 \, x^{4} + 1064845635750 \, x^{3} - 132753874800 \, x^{2} - 317609203475 \, x - 77754195847}{8134588 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} - \frac{2515625}{1331} \, \log \left (5 \, x + 3\right ) + \frac{222359715}{117649} \, \log \left (3 \, x + 2\right ) - \frac{15040}{156590819} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/8134588*(830228340600*x^5 + 1771154199360*x^4 + 1064845635750*x^3 - 132753874
800*x^2 - 317609203475*x - 77754195847)/(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3
- 392*x^2 - 272*x - 48) - 2515625/1331*log(5*x + 3) + 222359715/117649*log(3*x
+ 2) - 15040/156590819*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.217106, size = 234, normalized size = 2.41 \[ -\frac{63927582226200 \, x^{5} + 136378873350720 \, x^{4} + 81993113952750 \, x^{3} - 10222048359600 \, x^{2} + 1183843062500 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (5 \, x + 3\right ) - 1183843122660 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (3 \, x + 2\right ) + 60160 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (2 \, x - 1\right ) - 24455908667575 \, x - 5987073080219}{626363276 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/626363276*(63927582226200*x^5 + 136378873350720*x^4 + 81993113952750*x^3 - 10
222048359600*x^2 + 1183843062500*(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*
x^2 - 272*x - 48)*log(5*x + 3) - 1183843122660*(810*x^6 + 2241*x^5 + 2133*x^4 +
528*x^3 - 392*x^2 - 272*x - 48)*log(3*x + 2) + 60160*(810*x^6 + 2241*x^5 + 2133*
x^4 + 528*x^3 - 392*x^2 - 272*x - 48)*log(2*x - 1) - 24455908667575*x - 59870730
80219)/(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48)

_______________________________________________________________________________________

Sympy [A]  time = 0.752707, size = 85, normalized size = 0.88 \[ - \frac{830228340600 x^{5} + 1771154199360 x^{4} + 1064845635750 x^{3} - 132753874800 x^{2} - 317609203475 x - 77754195847}{6589016280 x^{6} + 18229611708 x^{5} + 17351076204 x^{4} + 4295062464 x^{3} - 3188758496 x^{2} - 2212607936 x - 390460224} - \frac{15040 \log{\left (x - \frac{1}{2} \right )}}{156590819} - \frac{2515625 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{222359715 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(830228340600*x**5 + 1771154199360*x**4 + 1064845635750*x**3 - 132753874800*x**
2 - 317609203475*x - 77754195847)/(6589016280*x**6 + 18229611708*x**5 + 17351076
204*x**4 + 4295062464*x**3 - 3188758496*x**2 - 2212607936*x - 390460224) - 15040
*log(x - 1/2)/156590819 - 2515625*log(x + 3/5)/1331 + 222359715*log(x + 2/3)/117
649

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208272, size = 140, normalized size = 1.44 \[ -\frac{15625}{121 \,{\left (5 \, x + 3\right )}} + \frac{25 \,{\left (\frac{6062344264539}{5 \, x + 3} + \frac{7964082495612}{{\left (5 \, x + 3\right )}^{2}} + \frac{3205106234076}{{\left (5 \, x + 3\right )}^{3}} + \frac{435889532968}{{\left (5 \, x + 3\right )}^{4}} - 1385260555122\right )}}{89480468 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + \frac{222359715}{117649} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{15040}{156590819} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15625/121/(5*x + 3) + 25/89480468*(6062344264539/(5*x + 3) + 7964082495612/(5*x
+ 3)^2 + 3205106234076/(5*x + 3)^3 + 435889532968/(5*x + 3)^4 - 1385260555122)/
((11/(5*x + 3) - 2)*(1/(5*x + 3) + 3)^4) + 222359715/117649*ln(abs(-1/(5*x + 3)
- 3)) - 15040/156590819*ln(abs(-11/(5*x + 3) + 2))