3.1710 \(\int \frac {1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^3} \, dx\)

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)-2054400/18947489099*ln(1-2*x)-115534350/117649*ln(2+3*x)[phone]/16105
1*ln(3+5*x)

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Rubi [A]  time = 0.06, antiderivative size = 108, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {15168}{246071287 (1-2 x)}+\frac {1944972}{16807 (3 x+2)}+\frac {1968750}{14641 (5 x+3)}+\frac {32}{3195731 (1-2 x)^2}+\frac {26973}{4802 (3 x+2)^2}-\frac {15625}{2662 (5 x+3)^2}+\frac {81}{343 (3 x+2)^3}-\frac {2054400 \log (1-2 x)}{18947489099}-\frac {115534350 \log (3 x+2)}{117649}+\frac {158156250 \log (5 x+3)}{161051} \]

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) + 194
4972/(16807*(2 + 3*x)) - 15625/(2662*(3 + 5*x)^2) + 1968750/(14641*(3 + 5*x)) - (2054400*Log[1 - 2*x])/1894748
9099 - (115534350*Log[2 + 3*x])/117649 + (158156250*Log[3 + 5*x])/161051

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^3} \, dx &=\int \left (-\frac {128}{3195731 (-1+2 x)^3}+\frac {30336}{246071287 (-1+2 x)^2}-\frac {4108800}{18947489099 (-1+2 x)}-\frac {729}{343 (2+3 x)^4}-\frac {80919}{2401 (2+3 x)^3}-\frac {5834916}{16807 (2+3 x)^2}-\frac {346603050}{117649 (2+3 x)}+\frac {78125}{1331 (3+5 x)^3}-\frac {9843750}{14641 (3+5 x)^2}+\frac {790781250}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {32}{3195731 (1-2 x)^2}+\frac {15168}{246071287 (1-2 x)}+\frac {81}{343 (2+3 x)^3}+\frac {26973}{4802 (2+3 x)^2}+\frac {1944972}{16807 (2+3 x)}-\frac {15625}{2662 (3+5 x)^2}+\frac {1968750}{14641 (3+5 x)}-\frac {2054400 \log (1-2 x)}{18947489099}-\frac {115534350 \log (2+3 x)}{117649}+\frac {158156250 \log (3+5 x)}{161051}\\ \end {align*}

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Mathematica [A]  time = 0.15, 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 + 13
6289326113000*x^5 + 86993245890000*x^6))/(3*(2 + 3*x)^3*(-3 + x + 10*x^2)^2) + 1369600*Log[3 - 6*x] + 12404615
067900*Log[2 + 3*x] - 12404616437500*Log[-3*(3 + 5*x)]))/37894978198

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fricas [B]  time = 0.73, size = 198, normalized size = 1.83 \[ \frac {6698479933530000 \, x^{6} + 10494278110701000 \, x^{5} + 1014683641656300 \, x^{4} - 5175447127123350 \, x^{3} - 1796782743686700 \, x^{2} + 37213849312500 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 37213845203700 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (3 \, x + 2\right ) - 4108800 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (2 \, x - 1\right ) + 635595472278305 \, x + 282301665291184}{37894978198 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/37894978198*(6698479933530000*x^6 + 10494278110701000*x^5 + 1014683641656300*x^4 - 5175447127123350*x^3 - 17
96782743686700*x^2 + 37213849312500*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x +
72)*log(5*x + 3) - 37213845203700*(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 + 282301665291184)/(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 +
276*x + 72)

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giac [A]  time = 1.24, size = 81, normalized size = 0.75 \[ \frac {86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {158156250}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {115534350}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {2054400}{18947489099} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

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, algorithm="giac")

[Out]

1/492142574*(86993245890000*x^6 + 136289326113000*x^5 + 13177709631900*x^4 - 67213599053550*x^3 - 233348408271
00*x^2 + 8254486652965*x + 3666255393392)/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)^2) + 158156250/161051*log(abs(5*x
+ 3)) - 115534350/117649*log(abs(3*x + 2)) - 2054400/18947489099*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 89, normalized size = 0.82 \[ -\frac {2054400 \ln \left (2 x -1\right )}{18947489099}-\frac {115534350 \ln \left (3 x +2\right )}{117649}+\frac {158156250 \ln \left (5 x +3\right )}{161051}-\frac {15625}{2662 \left (5 x +3\right )^{2}}+\frac {1968750}{14641 \left (5 x +3\right )}+\frac {81}{343 \left (3 x +2\right )^{3}}+\frac {26973}{4802 \left (3 x +2\right )^{2}}+\frac {1944972}{16807 \left (3 x +2\right )}+\frac {32}{3195731 \left (2 x -1\right )^{2}}-\frac {15168}{246071287 \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15625/2662/(5*x+3)^2+1968750/14641/(5*x+3)[phone]/161051*ln(5*x+3)+81/343/(3*x+2)^3+26973/4802/(3*x+2)^2+1
944972/16807/(3*x+2)-115534350/117649*ln(3*x+2)+32/3195731/(2*x-1)^2-15168/246071287/(2*x-1)-2054400/189474890
99*ln(2*x-1)

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maxima [A]  time = 0.56, size = 94, normalized size = 0.87 \[ \frac {86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} + \frac {158156250}{161051} \, \log \left (5 \, x + 3\right ) - \frac {115534350}{117649} \, \log \left (3 \, x + 2\right ) - \frac {2054400}{18947489099} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/492142574*(86993245890000*x^6 + 136289326113000*x^5 + 13177709631900*x^4 - 67213599053550*x^3 - 233348408271
00*x^2 + 8254486652965*x + 3666255393392)/(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 27
6*x + 72) + 158156250/161051*log(5*x + 3) - 115534350/117649*log(3*x + 2) - 2054400/18947489099*log(2*x - 1)

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mupad [B]  time = 0.05, size = 85, normalized size = 0.79 \[ \frac {158156250\,\ln \left (x+\frac {3}{5}\right )}{161051}-\frac {115534350\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {2054400\,\ln \left (x-\frac {1}{2}\right )}{18947489099}+\frac {\frac {16109860350\,x^6}{246071287}+\frac {25238764095\,x^5}{246071287}+\frac {443693927\,x^4}{44740234}-\frac {448090660357\,x^3}{8858566332}-\frac {2357054629\,x^2}{134220702}+\frac {687587393\,x}{110685960}+\frac {458281924174}{166098118725}}{x^7+\frac {11\,x^6}{5}+\frac {343\,x^5}{300}-\frac {457\,x^4}{675}-\frac {409\,x^3}{540}-\frac {101\,x^2}{1350}+\frac {23\,x}{225}+\frac {2}{75}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(158156250*log(x + 3/5))/161051 - (115534350*log(x + 2/3))/117649 - (2054400*log(x - 1/2))/18947489099 + ((687
587393*x)/110685960 - (2357054629*x^2)/134220702 - (448090660357*x^3)/8858566332 + (443693927*x^4)/44740234 +
(25238764095*x^5)/246071287 + (16109860350*x^6)/246071287 + 458281924174/166098118725)/((23*x)/225 - (101*x^2)
/1350 - (409*x^3)/540 - (457*x^4)/675 + (343*x^5)/300 + (11*x^6)/5 + x^7 + 2/75)

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sympy [A]  time = 0.31, 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 + 67213599053550*x**3 + 23334840827100*x**
2 - 8254486652965*x - 3666255393392)/(1328784949800*x**7 + 2923326889560*x**6 + 1519244125938*x**5 - 899636625
272*x**4 - 1006431563830*x**3 - 99412799948*x**2 + 135831350424*x + 35434265328) - 2054400*log(x - 1/2)/189474
89099 + 158156250*log(x + 3/5)/161051 - 115534350*log(x + 2/3)/117649

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