3.1665 \(\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=75 \[ \frac{1072}{290521 (1-2 x)}+\frac{1107}{2401 (3 x+2)}+\frac{4}{3773 (1-2 x)^2}+\frac{27}{686 (3 x+2)^2}-\frac{89792 \log (1-2 x)}{22370117}-\frac{39393 \log (3 x+2)}{16807}+\frac{3125 \log (5 x+3)}{1331} \]

[Out]

4/(3773*(1 - 2*x)^2) + 1072/(290521*(1 - 2*x)) + 27/(686*(2 + 3*x)^2) + 1107/(24
01*(2 + 3*x)) - (89792*Log[1 - 2*x])/22370117 - (39393*Log[2 + 3*x])/16807 + (31
25*Log[3 + 5*x])/1331

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Rubi [A]  time = 0.0866764, 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 \[ \frac{1072}{290521 (1-2 x)}+\frac{1107}{2401 (3 x+2)}+\frac{4}{3773 (1-2 x)^2}+\frac{27}{686 (3 x+2)^2}-\frac{89792 \log (1-2 x)}{22370117}-\frac{39393 \log (3 x+2)}{16807}+\frac{3125 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

4/(3773*(1 - 2*x)^2) + 1072/(290521*(1 - 2*x)) + 27/(686*(2 + 3*x)^2) + 1107/(24
01*(2 + 3*x)) - (89792*Log[1 - 2*x])/22370117 - (39393*Log[2 + 3*x])/16807 + (31
25*Log[3 + 5*x])/1331

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Rubi in Sympy [A]  time = 11.4603, size = 63, normalized size = 0.84 \[ - \frac{89792 \log{\left (- 2 x + 1 \right )}}{22370117} - \frac{39393 \log{\left (3 x + 2 \right )}}{16807} + \frac{3125 \log{\left (5 x + 3 \right )}}{1331} + \frac{1107}{2401 \left (3 x + 2\right )} + \frac{27}{686 \left (3 x + 2\right )^{2}} + \frac{1072}{290521 \left (- 2 x + 1\right )} + \frac{4}{3773 \left (- 2 x + 1\right )^{2}} \]

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),x)

[Out]

-89792*log(-2*x + 1)/22370117 - 39393*log(3*x + 2)/16807 + 3125*log(5*x + 3)/133
1 + 1107/(2401*(3*x + 2)) + 27/(686*(3*x + 2)**2) + 1072/(290521*(-2*x + 1)) + 4
/(3773*(-2*x + 1)**2)

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Mathematica [A]  time = 0.104706, size = 58, normalized size = 0.77 \[ \frac{\frac{77 \left (3176136 x^3-1006716 x^2-1414978 x+569697\right )}{\left (6 x^2+x-2\right )^2}-179584 \log (5-10 x)-104864166 \log (5 (3 x+2))[phone] \log (5 x+3)}{44740234} \]

Antiderivative was successfully verified.

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

[Out]

((77*(569697 - 1414978*x - 1006716*x^2 + 3176136*x^3))/(-2 + x + 6*x^2)^2 - 1795
84*Log[5 - 10*x] - 104864166*Log[5*(2 + 3*x)] + 105043750*Log[3 + 5*x])/44740234

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Maple [A]  time = 0.017, size = 62, normalized size = 0.8 \[{\frac{3125\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27}{686\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1107}{4802+7203\,x}}-{\frac{39393\,\ln \left ( 2+3\,x \right ) }{16807}}+{\frac{4}{3773\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{1072}{-290521+581042\,x}}-{\frac{89792\,\ln \left ( -1+2\,x \right ) }{22370117}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3125/1331*ln(3+5*x)+27/686/(2+3*x)^2+1107/2401/(2+3*x)-39393/16807*ln(2+3*x)+4/3
773/(-1+2*x)^2-1072/290521/(-1+2*x)-89792/22370117*ln(-1+2*x)

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Maxima [A]  time = 1.35602, size = 86, normalized size = 1.15 \[ \frac{3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac{3125}{1331} \, \log \left (5 \, x + 3\right ) - \frac{39393}{16807} \, \log \left (3 \, x + 2\right ) - \frac{89792}{22370117} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/581042*(3176136*x^3 - 1006716*x^2 - 1414978*x + 569697)/(36*x^4 + 12*x^3 - 23*
x^2 - 4*x + 4) + 3125/1331*log(5*x + 3) - 39393/16807*log(3*x + 2) - 89792/22370
117*log(2*x - 1)

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Fricas [A]  time = 0.22097, size = 166, normalized size = 2.21 \[ \frac{244562472 \, x^{3} - 77517132 \, x^{2} + 105043750 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 104864166 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 179584 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 108953306 \, x + 43866669}{44740234 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/44740234*(244562472*x^3 - 77517132*x^2 + 105043750*(36*x^4 + 12*x^3 - 23*x^2 -
4*x + 4)*log(5*x + 3) - 104864166*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(3*x
+ 2) - 179584*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 108953306*x +
43866669)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)

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Sympy [A]  time = 0.606914, size = 65, normalized size = 0.87 \[ \frac{3176136 x^{3} - 1006716 x^{2} - 1414978 x + 569697}{20917512 x^{4} + 6972504 x^{3} - 13363966 x^{2} - 2324168 x + 2324168} - \frac{89792 \log{\left (x - \frac{1}{2} \right )}}{22370117} + \frac{3125 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{39393 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(3176136*x**3 - 1006716*x**2 - 1414978*x + 569697)/(20917512*x**4 + 6972504*x**3
- 13363966*x**2 - 2324168*x + 2324168) - 89792*log(x - 1/2)/22370117 + 3125*log
(x + 3/5)/1331 - 39393*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.213359, size = 80, normalized size = 1.07 \[ \frac{3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \,{\left (3 \, x + 2\right )}^{2}{\left (2 \, x - 1\right )}^{2}} + \frac{3125}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{39393}{16807} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{89792}{22370117} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/581042*(3176136*x^3 - 1006716*x^2 - 1414978*x + 569697)/((3*x + 2)^2*(2*x - 1)
^2) + 3125/1331*ln(abs(5*x + 3)) - 39393/16807*ln(abs(3*x + 2)) - 89792/22370117
*ln(abs(2*x - 1))