3.1610 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=75 \[ \frac{16}{65219 (1-2 x)}+\frac{81}{49 (3 x+2)}+\frac{7750}{1331 (5 x+3)}-\frac{125}{242 (5 x+3)^2}-\frac{2736 \log (1-2 x)}{5021863}-\frac{8829}{343} \log (3 x+2)+\frac{376875 \log (5 x+3)}{14641} \]

[Out]

16/(65219*(1 - 2*x)) + 81/(49*(2 + 3*x)) - 125/(242*(3 + 5*x)^2) + 7750/(1331*(3
+ 5*x)) - (2736*Log[1 - 2*x])/5021863 - (8829*Log[2 + 3*x])/343 + (376875*Log[3
+ 5*x])/14641

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Rubi [A]  time = 0.0872994, 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 \[ \frac{16}{65219 (1-2 x)}+\frac{81}{49 (3 x+2)}+\frac{7750}{1331 (5 x+3)}-\frac{125}{242 (5 x+3)^2}-\frac{2736 \log (1-2 x)}{5021863}-\frac{8829}{343} \log (3 x+2)+\frac{376875 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

16/(65219*(1 - 2*x)) + 81/(49*(2 + 3*x)) - 125/(242*(3 + 5*x)^2) + 7750/(1331*(3
+ 5*x)) - (2736*Log[1 - 2*x])/5021863 - (8829*Log[2 + 3*x])/343 + (376875*Log[3
+ 5*x])/14641

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Rubi in Sympy [A]  time = 11.4412, size = 60, normalized size = 0.8 \[ - \frac{2736 \log{\left (- 2 x + 1 \right )}}{5021863} - \frac{8829 \log{\left (3 x + 2 \right )}}{343} + \frac{376875 \log{\left (5 x + 3 \right )}}{14641} + \frac{7750}{1331 \left (5 x + 3\right )} - \frac{125}{242 \left (5 x + 3\right )^{2}} + \frac{81}{49 \left (3 x + 2\right )} + \frac{16}{65219 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2736*log(-2*x + 1)/5021863 - 8829*log(3*x + 2)/343 + 376875*log(5*x + 3)/14641
+ 7750/(1331*(5*x + 3)) - 125/(242*(5*x + 3)**2) + 81/(49*(3*x + 2)) + 16/(65219
*(-2*x + 1))

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Mathematica [A]  time = 0.108413, size = 65, normalized size = 0.87 \[ \frac{\frac{77 \left (33563700 x^3+24606540 x^2-7974123 x-6363424\right )}{(5 x+3)^2 \left (6 x^2+x-2\right )}-5472 \log (5-10 x)-258530778 \log (5 (3 x+2))[phone] \log (5 x+3)}{10043726} \]

Antiderivative was successfully verified.

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

[Out]

((77*(-6363424 - 7974123*x + 24606540*x^2 + 33563700*x^3))/((3 + 5*x)^2*(-2 + x
+ 6*x^2)) - 5472*Log[5 - 10*x] - 258530778*Log[5*(2 + 3*x)] + 258536250*Log[3 +
5*x])/10043726

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Maple [A]  time = 0.019, size = 62, normalized size = 0.8 \[ -{\frac{125}{242\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{7750}{3993+6655\,x}}+{\frac{376875\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{81}{98+147\,x}}-{\frac{8829\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{16}{-65219+130438\,x}}-{\frac{2736\,\ln \left ( -1+2\,x \right ) }{5021863}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/242/(3+5*x)^2+7750/1331/(3+5*x)+376875/14641*ln(3+5*x)+81/49/(2+3*x)-8829/3
43*ln(2+3*x)-16/65219/(-1+2*x)-2736/5021863*ln(-1+2*x)

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Maxima [A]  time = 1.35071, size = 86, normalized size = 1.15 \[ \frac{33563700 \, x^{3} + 24606540 \, x^{2} - 7974123 \, x - 6363424}{130438 \,{\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )}} + \frac{376875}{14641} \, \log \left (5 \, x + 3\right ) - \frac{8829}{343} \, \log \left (3 \, x + 2\right ) - \frac{2736}{5021863} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/130438*(33563700*x^3 + 24606540*x^2 - 7974123*x - 6363424)/(150*x^4 + 205*x^3
+ 34*x^2 - 51*x - 18) + 376875/14641*log(5*x + 3) - 8829/343*log(3*x + 2) - 2736
/5021863*log(2*x - 1)

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Fricas [A]  time = 0.221142, size = 166, normalized size = 2.21 \[ \frac{2584404900 \, x^{3} + 1894703580 \, x^{2} + 258536250 \,{\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (5 \, x + 3\right ) - 258530778 \,{\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (3 \, x + 2\right ) - 5472 \,{\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (2 \, x - 1\right ) - 614007471 \, x - 489983648}{10043726 \,{\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10043726*(2584404900*x^3 + 1894703580*x^2 + 258536250*(150*x^4 + 205*x^3 + 34*
x^2 - 51*x - 18)*log(5*x + 3) - 258530778*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 1
8)*log(3*x + 2) - 5472*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log(2*x - 1) - 6
14007471*x - 489983648)/(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)

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Sympy [A]  time = 0.607219, size = 65, normalized size = 0.87 \[ \frac{33563700 x^{3} + 24606540 x^{2} - 7974123 x - 6363424}{19565700 x^{4} + 26739790 x^{3} + 4434892 x^{2} - 6652338 x - 2347884} - \frac{2736 \log{\left (x - \frac{1}{2} \right )}}{5021863} + \frac{376875 \log{\left (x + \frac{3}{5} \right )}}{14641} - \frac{8829 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(33563700*x**3 + 24606540*x**2 - 7974123*x - 6363424)/(19565700*x**4 + 26739790*
x**3 + 4434892*x**2 - 6652338*x - 2347884) - 2736*log(x - 1/2)/5021863 + 376875*
log(x + 3/5)/14641 - 8829*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.206674, size = 116, normalized size = 1.55 \[ \frac{81}{49 \,{\left (3 \, x + 2\right )}} + \frac{27 \,{\left (\frac{139939165}{3 \, x + 2} - \frac{31679854}{{\left (3 \, x + 2\right )}^{2}} - 37396350\right )}}{913066 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{376875}{14641} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{2736}{5021863} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/49/(3*x + 2) + 27/913066*(139939165/(3*x + 2) - 31679854/(3*x + 2)^2 - 373963
50)/((7/(3*x + 2) - 2)*(1/(3*x + 2) - 5)^2) + 376875/14641*ln(abs(-1/(3*x + 2) +
5)) - 2736/5021863*ln(abs(-7/(3*x + 2) + 2))