3.1677 \(\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=75 \[ \frac{1088}{456533 (1-2 x)}-\frac{81}{343 (3 x+2)}-\frac{625}{1331 (5 x+3)}+\frac{4}{5929 (1-2 x)^2}-\frac{92496 \log (1-2 x)}{35153041}+\frac{6156 \log (3 x+2)}{2401}-\frac{37500 \log (5 x+3)}{14641} \]

[Out]

4/(5929*(1 - 2*x)^2) + 1088/(456533*(1 - 2*x)) - 81/(343*(2 + 3*x)) - 625/(1331*
(3 + 5*x)) - (92496*Log[1 - 2*x])/35153041 + (6156*Log[2 + 3*x])/2401 - (37500*L
og[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi [A]  time = 0.0877557, antiderivative size = 75, 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 \[ \frac{1088}{456533 (1-2 x)}-\frac{81}{343 (3 x+2)}-\frac{625}{1331 (5 x+3)}+\frac{4}{5929 (1-2 x)^2}-\frac{92496 \log (1-2 x)}{35153041}+\frac{6156 \log (3 x+2)}{2401}-\frac{37500 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

4/(5929*(1 - 2*x)^2) + 1088/(456533*(1 - 2*x)) - 81/(343*(2 + 3*x)) - 625/(1331*
(3 + 5*x)) - (92496*Log[1 - 2*x])/35153041 + (6156*Log[2 + 3*x])/2401 - (37500*L
og[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 11.3953, size = 60, normalized size = 0.8 \[ - \frac{92496 \log{\left (- 2 x + 1 \right )}}{35153041} + \frac{6156 \log{\left (3 x + 2 \right )}}{2401} - \frac{37500 \log{\left (5 x + 3 \right )}}{14641} - \frac{625}{1331 \left (5 x + 3\right )} - \frac{81}{343 \left (3 x + 2\right )} + \frac{1088}{456533 \left (- 2 x + 1\right )} + \frac{4}{5929 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-92496*log(-2*x + 1)/35153041 + 6156*log(3*x + 2)/2401 - 37500*log(5*x + 3)/1464
1 - 625/(1331*(5*x + 3)) - 81/(343*(3*x + 2)) + 1088/(456533*(-2*x + 1)) + 4/(59
29*(-2*x + 1)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.113023, size = 68, normalized size = 0.91 \[ \frac{2 \left (77 \left (-\frac{107811}{6 x+4}-\frac{214375}{10 x+6}+\frac{544}{1-2 x}+\frac{154}{(1-2 x)^2}\right )-46248 \log (1-2 x)[phone] \log (6 x+4)-45018750 \log (10 x+6)\right )}{35153041} \]

Antiderivative was successfully verified.

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

[Out]

(2*(77*(154/(1 - 2*x)^2 + 544/(1 - 2*x) - 107811/(4 + 6*x) - 214375/(6 + 10*x))
- 46248*Log[1 - 2*x] + 45064998*Log[4 + 6*x] - 45018750*Log[6 + 10*x]))/35153041

_______________________________________________________________________________________

Maple [A]  time = 0.019, size = 62, normalized size = 0.8 \[ -{\frac{625}{3993+6655\,x}}-{\frac{37500\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{81}{686+1029\,x}}+{\frac{6156\,\ln \left ( 2+3\,x \right ) }{2401}}+{\frac{4}{5929\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{1088}{-456533+913066\,x}}-{\frac{92496\,\ln \left ( -1+2\,x \right ) }{35153041}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/1331/(3+5*x)-37500/14641*ln(3+5*x)-81/343/(2+3*x)+6156/2401*ln(2+3*x)+4/592
9/(-1+2*x)^2-1088/456533/(-1+2*x)-92496/35153041*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.36466, size = 86, normalized size = 1.15 \[ -\frac{4761360 \, x^{3} - 1699584 \, x^{2} - 1840020 \, x + 743807}{456533 \,{\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )}} - \frac{37500}{14641} \, \log \left (5 \, x + 3\right ) + \frac{6156}{2401} \, \log \left (3 \, x + 2\right ) - \frac{92496}{35153041} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/456533*(4761360*x^3 - 1699584*x^2 - 1840020*x + 743807)/(60*x^4 + 16*x^3 - 37
*x^2 - 5*x + 6) - 37500/14641*log(5*x + 3) + 6156/2401*log(3*x + 2) - 92496/3515
3041*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.214603, size = 166, normalized size = 2.21 \[ -\frac{366624720 \, x^{3} - 130867968 \, x^{2} + 90037500 \,{\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 90129996 \,{\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 92496 \,{\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (2 \, x - 1\right ) - 141681540 \, x + 57273139}{35153041 \,{\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/35153041*(366624720*x^3 - 130867968*x^2 + 90037500*(60*x^4 + 16*x^3 - 37*x^2
- 5*x + 6)*log(5*x + 3) - 90129996*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(3*x
+ 2) + 92496*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(2*x - 1) - 141681540*x + 5
7273139)/(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)

_______________________________________________________________________________________

Sympy [A]  time = 0.613928, size = 65, normalized size = 0.87 \[ - \frac{4761360 x^{3} - 1699584 x^{2} - 1840020 x + 743807}{27391980 x^{4} + 7304528 x^{3} - 16891721 x^{2} - 2282665 x + 2739198} - \frac{92496 \log{\left (x - \frac{1}{2} \right )}}{35153041} - \frac{37500 \log{\left (x + \frac{3}{5} \right )}}{14641} + \frac{6156 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(4761360*x**3 - 1699584*x**2 - 1840020*x + 743807)/(27391980*x**4 + 7304528*x**
3 - 16891721*x**2 - 2282665*x + 2739198) - 92496*log(x - 1/2)/35153041 - 37500*l
og(x + 3/5)/14641 + 6156*log(x + 2/3)/2401

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21322, size = 116, normalized size = 1.55 \[ -\frac{625}{1331 \,{\left (5 \, x + 3\right )}} - \frac{5 \,{\left (\frac{156456196}{5 \, x + 3} - \frac{430519419}{{\left (5 \, x + 3\right )}^{2}} - 14216316\right )}}{5021863 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}{\left (\frac{1}{5 \, x + 3} + 3\right )}} + \frac{6156}{2401} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{92496}{35153041} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/1331/(5*x + 3) - 5/5021863*(156456196/(5*x + 3) - 430519419/(5*x + 3)^2 - 1
4216316)/((11/(5*x + 3) - 2)^2*(1/(5*x + 3) + 3)) + 6156/2401*ln(abs(-1/(5*x + 3
) - 3)) - 92496/35153041*ln(abs(-11/(5*x + 3) + 2))