3.1693 \(\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^3} \, dx\)

Optimal. Leaf size=108 \[ \frac{15168}{246071287 (1-2 x)}+\frac{1944972}{16807 (3 x+2)}+\frac{1968750}{14641 (5 x+3)}+\frac{32}{3195731 (1-2 x)^2}+\frac{26973}{4802 (3 x+2)^2}-\frac{15625}{2662 (5 x+3)^2}+\frac{81}{343 (3 x+2)^3}-\frac{2054400 \log (1-2 x)}{18947489099}-\frac{115534350 \log (3 x+2)}{117649}+\frac{158156250 \log (5 x+3)}{161051} \]

[Out]

32/(3195731*(1 - 2*x)^2) + 15168/(246071287*(1 - 2*x)) + 81/(343*(2 + 3*x)^3) +
26973/(4802*(2 + 3*x)^2) + 1944972/(16807*(2 + 3*x)) - 15625/(2662*(3 + 5*x)^2)
+ 1968750/(14641*(3 + 5*x)) - (2054400*Log[1 - 2*x])/18947489099 - (115534350*Lo
g[2 + 3*x])/117649 + (158156250*Log[3 + 5*x])/161051

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Rubi [A]  time = 0.138861, antiderivative size = 108, 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 \[ \frac{15168}{246071287 (1-2 x)}+\frac{1944972}{16807 (3 x+2)}+\frac{1968750}{14641 (5 x+3)}+\frac{32}{3195731 (1-2 x)^2}+\frac{26973}{4802 (3 x+2)^2}-\frac{15625}{2662 (5 x+3)^2}+\frac{81}{343 (3 x+2)^3}-\frac{2054400 \log (1-2 x)}{18947489099}-\frac{115534350 \log (3 x+2)}{117649}+\frac{158156250 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

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

[Out]

32/(3195731*(1 - 2*x)^2) + 15168/(246071287*(1 - 2*x)) + 81/(343*(2 + 3*x)^3) +
26973/(4802*(2 + 3*x)^2) + 1944972/(16807*(2 + 3*x)) - 15625/(2662*(3 + 5*x)^2)
+ 1968750/(14641*(3 + 5*x)) - (2054400*Log[1 - 2*x])/18947489099 - (115534350*Lo
g[2 + 3*x])/117649 + (158156250*Log[3 + 5*x])/161051

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Rubi in Sympy [A]  time = 16.3087, size = 90, normalized size = 0.83 \[ - \frac{2054400 \log{\left (- 2 x + 1 \right )}}{18947489099} - \frac{115534350 \log{\left (3 x + 2 \right )}}{117649} + \frac{158156250 \log{\left (5 x + 3 \right )}}{161051} + \frac{1968750}{14641 \left (5 x + 3\right )} - \frac{15625}{2662 \left (5 x + 3\right )^{2}} + \frac{1944972}{16807 \left (3 x + 2\right )} + \frac{26973}{4802 \left (3 x + 2\right )^{2}} + \frac{81}{343 \left (3 x + 2\right )^{3}} + \frac{15168}{246071287 \left (- 2 x + 1\right )} + \frac{32}{3195731 \left (- 2 x + 1\right )^{2}} \]

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)**3,x)

[Out]

-2054400*log(-2*x + 1)/18947489099 - 115534350*log(3*x + 2)/117649 + 158156250*l
og(5*x + 3)/161051 + 1968750/(14641*(5*x + 3)) - 15625/(2662*(5*x + 3)**2) + 194
4972/(16807*(3*x + 2)) + 26973/(4802*(3*x + 2)**2) + 81/(343*(3*x + 2)**3) + 151
68/(246071287*(-2*x + 1)) + 32/(3195731*(-2*x + 1)**2)

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Mathematica [A]  time = 0.177297, size = 82, normalized size = 0.76 \[ -\frac{3 \left (-\frac{77 \left (86993245890000 x^6+136289326113000 x^5+13177709631900 x^4-67213599053550 x^3-23334840827100 x^2+8254486652965 x+3666255393392\right )}{3 (3 x+2)^3 \left (10 x^2+x-3\right )^2}+1369600 \log (3-6 x)[phone] \log (3 x+2)-12404616437500 \log (-3 (5 x+3))\right )}{37894978198} \]

Antiderivative was successfully verified.

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

[Out]

(-3*((-77*(3666255393392 + 8254486652965*x - 23334840827100*x^2 - 67213599053550
*x^3 + 13177709631900*x^4 + 136289326113000*x^5 + 86993245890000*x^6))/(3*(2 + 3
*x)^3*(-3 + x + 10*x^2)^2) + 1369600*Log[3 - 6*x] + 12404615067900*Log[2 + 3*x]
- 12404616437500*Log[-3*(3 + 5*x)]))/37894978198

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Maple [A]  time = 0.02, size = 89, normalized size = 0.8 \[ -{\frac{15625}{2662\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{1968750}{43923+73205\,x}}+{\frac{158156250\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{81}{343\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{26973}{4802\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1944972}{33614+50421\,x}}-{\frac{115534350\,\ln \left ( 2+3\,x \right ) }{117649}}+{\frac{32}{3195731\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{15168}{-246071287+492142574\,x}}-{\frac{2054400\,\ln \left ( -1+2\,x \right ) }{18947489099}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15625/2662/(3+5*x)^2+1968750/14641/(3+5*x)[phone]/161051*ln(3+5*x)+81/343/(2
+3*x)^3+26973/4802/(2+3*x)^2+1944972/16807/(2+3*x)-115534350/117649*ln(2+3*x)+32
/3195731/(-1+2*x)^2-15168/246071287/(-1+2*x)-2054400/18947489099*ln(-1+2*x)

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Maxima [A]  time = 1.34058, size = 127, normalized size = 1.18 \[ \frac{86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \,{\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} + \frac{158156250}{161051} \, \log \left (5 \, x + 3\right ) - \frac{115534350}{117649} \, \log \left (3 \, x + 2\right ) - \frac{2054400}{18947489099} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/492142574*(86993245890000*x^6 + 136289326113000*x^5 + 13177709631900*x^4 - 672
13599053550*x^3 - 23334840827100*x^2 + 8254486652965*x + 3666255393392)/(2700*x^
7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72) + 15815625
0/161051*log(5*x + 3) - 115534350/117649*log(3*x + 2) - 2054400/18947489099*log(
2*x - 1)

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Fricas [A]  time = 0.21905, size = 267, normalized size = 2.47 \[ \frac{6698479933530000 \, x^{6} + 10494278110701000 \, x^{5} + 1014683641656300 \, x^{4} - 5175447127123350 \, x^{3} - 1796782743686700 \, x^{2} + 37213849312500 \,{\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 37213845203700 \,{\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (3 \, x + 2\right ) - 4108800 \,{\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (2 \, x - 1\right ) + 635595472278305 \, x + 282301665291184}{37894978198 \,{\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/37894978198*(6698479933530000*x^6 + 10494278110701000*x^5 + 1014683641656300*x
^4 - 5175447127123350*x^3 - 1796782743686700*x^2 + 37213849312500*(2700*x^7 + 59
40*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72)*log(5*x + 3) - 3
7213845203700*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 +
276*x + 72)*log(3*x + 2) - 4108800*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 -
2045*x^3 - 202*x^2 + 276*x + 72)*log(2*x - 1) + 635595472278305*x + 282301665291
184)/(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 7
2)

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Sympy [A]  time = 0.842713, size = 95, normalized size = 0.88 \[ \frac{86993245890000 x^{6} + 136289326113000 x^{5} + 13177709631900 x^{4} - 67213599053550 x^{3} - 23334840827100 x^{2} + 8254486652965 x + 3666255393392}{1328784949800 x^{7} + 2923326889560 x^{6} + 1519244125938 x^{5} - 899636625272 x^{4} - 1006431563830 x^{3} - 99412799948 x^{2} + 135831350424 x + 35434265328} - \frac{2054400 \log{\left (x - \frac{1}{2} \right )}}{18947489099} + \frac{158156250 \log{\left (x + \frac{3}{5} \right )}}{161051} - \frac{115534350 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(86993245890000*x**6 + 136289326113000*x**5 + 13177709631900*x**4 - 672135990535
50*x**3 - 23334840827100*x**2 + 8254486652965*x + 3666255393392)/(1328784949800*
x**7 + 2923326889560*x**6 + 1519244125938*x**5 - 899636625272*x**4 - 10064315638
30*x**3 - 99412799948*x**2 + 135831350424*x + 35434265328) - 2054400*log(x - 1/2
)/18947489099 + 158156250*log(x + 3/5)/161051 - 115534350*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.210542, size = 109, normalized size = 1.01 \[ \frac{86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{158156250}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{115534350}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{2054400}{18947489099} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/492142574*(86993245890000*x^6 + 136289326113000*x^5 + 13177709631900*x^4 - 672
13599053550*x^3 - 23334840827100*x^2 + 8254486652965*x + 3666255393392)/((5*x +
3)^2*(3*x + 2)^3*(2*x - 1)^2) + 158156250/161051*ln(abs(5*x + 3)) - 115534350/11
7649*ln(abs(3*x + 2)) - 2054400/18947489099*ln(abs(2*x - 1))