3.1595 \(\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^2} \, dx\)

Optimal. Leaf size=53 \[ \frac{4}{847 (1-2 x)}-\frac{25}{121 (5 x+3)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331} \]

[Out]

4/(847*(1 - 2*x)) - 25/(121*(3 + 5*x)) - (412*Log[1 - 2*x])/65219 + (27*Log[2 +
3*x])/49 - (725*Log[3 + 5*x])/1331

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Rubi [A]  time = 0.0623055, antiderivative size = 53, 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 \[ \frac{4}{847 (1-2 x)}-\frac{25}{121 (5 x+3)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

4/(847*(1 - 2*x)) - 25/(121*(3 + 5*x)) - (412*Log[1 - 2*x])/65219 + (27*Log[2 +
3*x])/49 - (725*Log[3 + 5*x])/1331

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Rubi in Sympy [A]  time = 8.79424, size = 42, normalized size = 0.79 \[ - \frac{412 \log{\left (- 2 x + 1 \right )}}{65219} + \frac{27 \log{\left (3 x + 2 \right )}}{49} - \frac{725 \log{\left (5 x + 3 \right )}}{1331} - \frac{25}{121 \left (5 x + 3\right )} + \frac{4}{847 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-412*log(-2*x + 1)/65219 + 27*log(3*x + 2)/49 - 725*log(5*x + 3)/1331 - 25/(121*
(5*x + 3)) + 4/(847*(-2*x + 1))

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Mathematica [A]  time = 0.0574241, size = 48, normalized size = 0.91 \[ \frac{-\frac{77 (370 x-163)}{10 x^2+x-3}-412 \log (3-6 x)+35937 \log (3 x+2)-35525 \log (-3 (5 x+3))}{65219} \]

Antiderivative was successfully verified.

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

[Out]

((-77*(-163 + 370*x))/(-3 + x + 10*x^2) - 412*Log[3 - 6*x] + 35937*Log[2 + 3*x]
- 35525*Log[-3*(3 + 5*x)])/65219

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Maple [A]  time = 0.017, size = 44, normalized size = 0.8 \[ -{\frac{25}{363+605\,x}}-{\frac{725\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{4}{-847+1694\,x}}-{\frac{412\,\ln \left ( -1+2\,x \right ) }{65219}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/121/(3+5*x)-725/1331*ln(3+5*x)+27/49*ln(2+3*x)-4/847/(-1+2*x)-412/65219*ln(-
1+2*x)

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Maxima [A]  time = 1.34895, size = 57, normalized size = 1.08 \[ -\frac{370 \, x - 163}{847 \,{\left (10 \, x^{2} + x - 3\right )}} - \frac{725}{1331} \, \log \left (5 \, x + 3\right ) + \frac{27}{49} \, \log \left (3 \, x + 2\right ) - \frac{412}{65219} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/847*(370*x - 163)/(10*x^2 + x - 3) - 725/1331*log(5*x + 3) + 27/49*log(3*x +
2) - 412/65219*log(2*x - 1)

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Fricas [A]  time = 0.219165, size = 88, normalized size = 1.66 \[ -\frac{35525 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 35937 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (3 \, x + 2\right ) + 412 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) + 28490 \, x - 12551}{65219 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/65219*(35525*(10*x^2 + x - 3)*log(5*x + 3) - 35937*(10*x^2 + x - 3)*log(3*x +
2) + 412*(10*x^2 + x - 3)*log(2*x - 1) + 28490*x - 12551)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.470787, size = 44, normalized size = 0.83 \[ - \frac{370 x - 163}{8470 x^{2} + 847 x - 2541} - \frac{412 \log{\left (x - \frac{1}{2} \right )}}{65219} - \frac{725 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{27 \log{\left (x + \frac{2}{3} \right )}}{49} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(370*x - 163)/(8470*x**2 + 847*x - 2541) - 412*log(x - 1/2)/65219 - 725*log(x +
3/5)/1331 + 27*log(x + 2/3)/49

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GIAC/XCAS [A]  time = 0.212083, size = 74, normalized size = 1.4 \[ -\frac{25}{121 \,{\left (5 \, x + 3\right )}} + \frac{40}{9317 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} + \frac{27}{49} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{412}{65219} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/121/(5*x + 3) + 40/9317/(11/(5*x + 3) - 2) + 27/49*ln(abs(-1/(5*x + 3) - 3))
- 412/65219*ln(abs(-11/(5*x + 3) + 2))