3.1494 \(\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=53 \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]

[Out]

-9/(7*(2 + 3*x)) - 25/(11*(3 + 5*x)) - (8*Log[1 - 2*x])/5929 + (648*Log[2 + 3*x]
)/49 - (1600*Log[3 + 5*x])/121

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Rubi [A]  time = 0.0633557, 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 \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-9/(7*(2 + 3*x)) - 25/(11*(3 + 5*x)) - (8*Log[1 - 2*x])/5929 + (648*Log[2 + 3*x]
)/49 - (1600*Log[3 + 5*x])/121

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Rubi in Sympy [A]  time = 8.73333, size = 42, normalized size = 0.79 \[ - \frac{8 \log{\left (- 2 x + 1 \right )}}{5929} + \frac{648 \log{\left (3 x + 2 \right )}}{49} - \frac{1600 \log{\left (5 x + 3 \right )}}{121} - \frac{25}{11 \left (5 x + 3\right )} - \frac{9}{7 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*log(-2*x + 1)/5929 + 648*log(3*x + 2)/49 - 1600*log(5*x + 3)/121 - 25/(11*(5*
x + 3)) - 9/(7*(3*x + 2))

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Mathematica [A]  time = 0.0394897, size = 47, normalized size = 0.89 \[ \frac{2 \left (-\frac{7623}{6 x+4}-\frac{13475}{10 x+6}-4 \log (1-2 x)+39204 \log (6 x+4)-39200 \log (10 x+6)\right )}{5929} \]

Antiderivative was successfully verified.

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

[Out]

(2*(-7623/(4 + 6*x) - 13475/(6 + 10*x) - 4*Log[1 - 2*x] + 39204*Log[4 + 6*x] - 3
9200*Log[6 + 10*x]))/5929

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Maple [A]  time = 0.016, size = 44, normalized size = 0.8 \[ -{\frac{25}{33+55\,x}}-{\frac{1600\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9}{14+21\,x}}+{\frac{648\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{8\,\ln \left ( -1+2\,x \right ) }{5929}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/11/(3+5*x)-1600/121*ln(3+5*x)-9/7/(2+3*x)+648/49*ln(2+3*x)-8/5929*ln(-1+2*x)

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Maxima [A]  time = 1.35516, size = 59, normalized size = 1.11 \[ -\frac{1020 \, x + 647}{77 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - \frac{1600}{121} \, \log \left (5 \, x + 3\right ) + \frac{648}{49} \, \log \left (3 \, x + 2\right ) - \frac{8}{5929} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/77*(1020*x + 647)/(15*x^2 + 19*x + 6) - 1600/121*log(5*x + 3) + 648/49*log(3*
x + 2) - 8/5929*log(2*x - 1)

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Fricas [A]  time = 0.219123, size = 99, normalized size = 1.87 \[ -\frac{78400 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 78408 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 8 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (2 \, x - 1\right ) + 78540 \, x + 49819}{5929 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5929*(78400*(15*x^2 + 19*x + 6)*log(5*x + 3) - 78408*(15*x^2 + 19*x + 6)*log(
3*x + 2) + 8*(15*x^2 + 19*x + 6)*log(2*x - 1) + 78540*x + 49819)/(15*x^2 + 19*x
+ 6)

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Sympy [A]  time = 0.501347, size = 44, normalized size = 0.83 \[ - \frac{1020 x + 647}{1155 x^{2} + 1463 x + 462} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{5929} - \frac{1600 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{648 \log{\left (x + \frac{2}{3} \right )}}{49} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1020*x + 647)/(1155*x**2 + 1463*x + 462) - 8*log(x - 1/2)/5929 - 1600*log(x +
3/5)/121 + 648*log(x + 2/3)/49

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GIAC/XCAS [A]  time = 0.219194, size = 72, normalized size = 1.36 \[ -\frac{25}{11 \,{\left (5 \, x + 3\right )}} + \frac{135}{7 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}} + \frac{648}{49} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{8}{5929} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/11/(5*x + 3) + 135/7/(1/(5*x + 3) + 3) + 648/49*ln(abs(-1/(5*x + 3) - 3)) -
8/5929*ln(abs(-11/(5*x + 3) + 2))