3.1692 \(\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=97 \[ \frac{6528}{35153041 (1-2 x)}+\frac{26973}{2401 (3 x+2)}+\frac{290625}{14641 (5 x+3)}+\frac{16}{456533 (1-2 x)^2}+\frac{243}{686 (3 x+2)^2}-\frac{3125}{2662 (5 x+3)^2}-\frac{776928 \log (1-2 x)}{2706784157}-\frac{1944972 \log (3 x+2)}{16807}+\frac{18637500 \log (5 x+3)}{161051} \]

[Out]

16/(456533*(1 - 2*x)^2) + 6528/(35153041*(1 - 2*x)) + 243/(686*(2 + 3*x)^2) + 26
973/(2401*(2 + 3*x)) - 3125/(2662*(3 + 5*x)^2) + 290625/(14641*(3 + 5*x)) - (776
928*Log[1 - 2*x])/2706784157 - (1944972*Log[2 + 3*x])/16807 + (18637500*Log[3 +
5*x])/161051

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Rubi [A]  time = 0.119966, 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 \[ \frac{6528}{35153041 (1-2 x)}+\frac{26973}{2401 (3 x+2)}+\frac{290625}{14641 (5 x+3)}+\frac{16}{456533 (1-2 x)^2}+\frac{243}{686 (3 x+2)^2}-\frac{3125}{2662 (5 x+3)^2}-\frac{776928 \log (1-2 x)}{2706784157}-\frac{1944972 \log (3 x+2)}{16807}+\frac{18637500 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

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

[Out]

16/(456533*(1 - 2*x)^2) + 6528/(35153041*(1 - 2*x)) + 243/(686*(2 + 3*x)^2) + 26
973/(2401*(2 + 3*x)) - 3125/(2662*(3 + 5*x)^2) + 290625/(14641*(3 + 5*x)) - (776
928*Log[1 - 2*x])/2706784157 - (1944972*Log[2 + 3*x])/16807 + (18637500*Log[3 +
5*x])/161051

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Rubi in Sympy [A]  time = 14.7127, size = 80, normalized size = 0.82 \[ - \frac{776928 \log{\left (- 2 x + 1 \right )}}{2706784157} - \frac{1944972 \log{\left (3 x + 2 \right )}}{16807} + \frac{18637500 \log{\left (5 x + 3 \right )}}{161051} + \frac{290625}{14641 \left (5 x + 3\right )} - \frac{3125}{2662 \left (5 x + 3\right )^{2}} + \frac{26973}{2401 \left (3 x + 2\right )} + \frac{243}{686 \left (3 x + 2\right )^{2}} + \frac{6528}{35153041 \left (- 2 x + 1\right )} + \frac{16}{456533 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-776928*log(-2*x + 1)/2706784157 - 1944972*log(3*x + 2)/16807 + 18637500*log(5*x
+ 3)/161051 + 290625/(14641*(5*x + 3)) - 3125/(2662*(5*x + 3)**2) + 26973/(2401
*(3*x + 2)) + 243/(686*(3*x + 2)**2) + 6528/(35153041*(-2*x + 1)) + 16/(456533*(
-2*x + 1)**2)

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Mathematica [A]  time = 0.242476, size = 88, normalized size = 0.91 \[ \frac{2 \left (\frac{77}{4} \left (\frac{789823386}{3 x+2}+\frac{1395581250}{5 x+3}+\frac{24904341}{(3 x+2)^2}-\frac{82534375}{(5 x+3)^2}+\frac{13056}{1-2 x}+\frac{2464}{(1-2 x)^2}\right )-388464 \log (1-2 x)-156619842786 \log (6 x+4)[phone] \log (10 x+6)\right )}{2706784157} \]

Antiderivative was successfully verified.

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

[Out]

(2*((77*(2464/(1 - 2*x)^2 + 13056/(1 - 2*x) + 24904341/(2 + 3*x)^2 + 789823386/(
2 + 3*x) - 82534375/(3 + 5*x)^2 + 1395581250/(3 + 5*x)))/4 - 388464*Log[1 - 2*x]
- 156619842786*Log[4 + 6*x] + 156620231250*Log[6 + 10*x]))/2706784157

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Maple [A]  time = 0.02, size = 80, normalized size = 0.8 \[ -{\frac{3125}{2662\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{290625}{43923+73205\,x}}+{\frac{18637500\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{243}{686\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{26973}{4802+7203\,x}}-{\frac{1944972\,\ln \left ( 2+3\,x \right ) }{16807}}+{\frac{16}{456533\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{6528}{-35153041+70306082\,x}}-{\frac{776928\,\ln \left ( -1+2\,x \right ) }{2706784157}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3125/2662/(3+5*x)^2+290625/14641/(3+5*x)[phone]/161051*ln(3+5*x)+243/686/(2+3
*x)^2+26973/2401/(2+3*x)-1944972/16807*ln(2+3*x)+16/456533/(-1+2*x)^2-6528/35153
041/(-1+2*x)-776928/2706784157*ln(-1+2*x)

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Maxima [A]  time = 1.35079, size = 113, normalized size = 1.16 \[ \frac{488145765600 \, x^{5} + 439319535120 \, x^{4} - 218954328504 \, x^{3} - 231191334456 \, x^{2} + 23195310772 \, x + 30858356237}{70306082 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} + \frac{18637500}{161051} \, \log \left (5 \, x + 3\right ) - \frac{1944972}{16807} \, \log \left (3 \, x + 2\right ) - \frac{776928}{2706784157} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/70306082*(488145765600*x^5 + 439319535120*x^4 - 218954328504*x^3 - 23119133445
6*x^2 + 23195310772*x + 30858356237)/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 2
27*x^2 + 84*x + 36) + 18637500/161051*log(5*x + 3) - 1944972/16807*log(3*x + 2)
- 776928/2706784157*log(2*x - 1)

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Fricas [A]  time = 0.228246, size = 234, normalized size = 2.41 \[ \frac{37587223951200 \, x^{5} + 33827604204240 \, x^{4} - 16859483294808 \, x^{3} - 17801732753112 \, x^{2} + 626480925000 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 626479371144 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (3 \, x + 2\right ) - 1553856 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (2 \, x - 1\right ) + 1786038929444 \, x + 2376093430249}{5413568314 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5413568314*(37587223951200*x^5 + 33827604204240*x^4 - 16859483294808*x^3 - 178
01732753112*x^2 + 626480925000*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2
+ 84*x + 36)*log(5*x + 3) - 626479371144*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^
3 - 227*x^2 + 84*x + 36)*log(3*x + 2) - 1553856*(900*x^6 + 1380*x^5 + 109*x^4 -
682*x^3 - 227*x^2 + 84*x + 36)*log(2*x - 1) + 1786038929444*x + 2376093430249)/(
900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)

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Sympy [A]  time = 0.757523, size = 85, normalized size = 0.88 \[ \frac{488145765600 x^{5} + 439319535120 x^{4} - 218954328504 x^{3} - 231191334456 x^{2} + 23195310772 x + 30858356237}{63275473800 x^{6} + 97022393160 x^{5} + 7663362938 x^{4} - 47948747924 x^{3} - 15959480614 x^{2} + 5905710888 x + 2531018952} - \frac{776928 \log{\left (x - \frac{1}{2} \right )}}{2706784157} + \frac{18637500 \log{\left (x + \frac{3}{5} \right )}}{161051} - \frac{1944972 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(488145765600*x**5 + 439319535120*x**4 - 218954328504*x**3 - 231191334456*x**2 +
23195310772*x + 30858356237)/(63275473800*x**6 + 97022393160*x**5 + 7663362938*
x**4 - 47948747924*x**3 - 15959480614*x**2 + 5905710888*x + 2531018952) - 776928
*log(x - 1/2)/2706784157 + 18637500*log(x + 3/5)/161051 - 1944972*log(x + 2/3)/1
6807

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GIAC/XCAS [A]  time = 0.211355, size = 97, normalized size = 1. \[ \frac{488145765600 \, x^{5} + 439319535120 \, x^{4} - 218954328504 \, x^{3} - 231191334456 \, x^{2} + 23195310772 \, x + 30858356237}{70306082 \,{\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}^{2}} + \frac{18637500}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1944972}{16807} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{776928}{2706784157} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/70306082*(488145765600*x^5 + 439319535120*x^4 - 218954328504*x^3 - 23119133445
6*x^2 + 23195310772*x + 30858356237)/(30*x^3 + 23*x^2 - 7*x - 6)^2 + 18637500/16
1051*ln(abs(5*x + 3)) - 1944972/16807*ln(abs(3*x + 2)) - 776928/2706784157*ln(ab
s(2*x - 1))