3.1549 \(\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^4} \, dx\)

Optimal. Leaf size=65 \[ \frac{242}{2401 (1-2 x)}-\frac{319}{2401 (3 x+2)}+\frac{11}{343 (3 x+2)^2}-\frac{1}{441 (3 x+2)^3}-\frac{1364 \log (1-2 x)}{16807}+\frac{1364 \log (3 x+2)}{16807} \]

[Out]

242/(2401*(1 - 2*x)) - 1/(441*(2 + 3*x)^3) + 11/(343*(2 + 3*x)^2) - 319/(2401*(2
+ 3*x)) - (1364*Log[1 - 2*x])/16807 + (1364*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0732982, antiderivative size = 65, 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 \[ \frac{242}{2401 (1-2 x)}-\frac{319}{2401 (3 x+2)}+\frac{11}{343 (3 x+2)^2}-\frac{1}{441 (3 x+2)^3}-\frac{1364 \log (1-2 x)}{16807}+\frac{1364 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^4),x]

[Out]

242/(2401*(1 - 2*x)) - 1/(441*(2 + 3*x)^3) + 11/(343*(2 + 3*x)^2) - 319/(2401*(2
+ 3*x)) - (1364*Log[1 - 2*x])/16807 + (1364*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 10.2282, size = 53, normalized size = 0.82 \[ - \frac{1364 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{1364 \log{\left (3 x + 2 \right )}}{16807} - \frac{319}{2401 \left (3 x + 2\right )} + \frac{11}{343 \left (3 x + 2\right )^{2}} - \frac{1}{441 \left (3 x + 2\right )^{3}} + \frac{242}{2401 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**4,x)

[Out]

-1364*log(-2*x + 1)/16807 + 1364*log(3*x + 2)/16807 - 319/(2401*(3*x + 2)) + 11/
(343*(3*x + 2)**2) - 1/(441*(3*x + 2)**3) + 242/(2401*(-2*x + 1))

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Mathematica [A]  time = 0.0655597, size = 54, normalized size = 0.83 \[ \frac{2 \left (-\frac{7 \left (110484 x^3+156519 x^2+66329 x+7277\right )}{2 (2 x-1) (3 x+2)^3}-6138 \log (1-2 x)+6138 \log (6 x+4)\right )}{151263} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^4),x]

[Out]

(2*((-7*(7277 + 66329*x + 156519*x^2 + 110484*x^3))/(2*(-1 + 2*x)*(2 + 3*x)^3) -
6138*Log[1 - 2*x] + 6138*Log[4 + 6*x]))/151263

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Maple [A]  time = 0.016, size = 54, normalized size = 0.8 \[ -{\frac{1}{441\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{11}{343\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{319}{4802+7203\,x}}+{\frac{1364\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{242}{-2401+4802\,x}}-{\frac{1364\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)^2/(2+3*x)^4,x)

[Out]

-1/441/(2+3*x)^3+11/343/(2+3*x)^2-319/2401/(2+3*x)+1364/16807*ln(2+3*x)-242/2401
/(-1+2*x)-1364/16807*ln(-1+2*x)

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Maxima [A]  time = 1.35311, size = 76, normalized size = 1.17 \[ -\frac{110484 \, x^{3} + 156519 \, x^{2} + 66329 \, x + 7277}{21609 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{1364}{16807} \, \log \left (3 \, x + 2\right ) - \frac{1364}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")

[Out]

-1/21609*(110484*x^3 + 156519*x^2 + 66329*x + 7277)/(54*x^4 + 81*x^3 + 18*x^2 -
20*x - 8) + 1364/16807*log(3*x + 2) - 1364/16807*log(2*x - 1)

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Fricas [A]  time = 0.215891, size = 128, normalized size = 1.97 \[ -\frac{773388 \, x^{3} + 1095633 \, x^{2} - 12276 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 12276 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 464303 \, x + 50939}{151263 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")

[Out]

-1/151263*(773388*x^3 + 1095633*x^2 - 12276*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8
)*log(3*x + 2) + 12276*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) + 4643
03*x + 50939)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)

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Sympy [A]  time = 0.425063, size = 54, normalized size = 0.83 \[ - \frac{110484 x^{3} + 156519 x^{2} + 66329 x + 7277}{1166886 x^{4} + 1750329 x^{3} + 388962 x^{2} - 432180 x - 172872} - \frac{1364 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{1364 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**4,x)

[Out]

-(110484*x**3 + 156519*x**2 + 66329*x + 7277)/(1166886*x**4 + 1750329*x**3 + 388
962*x**2 - 432180*x - 172872) - 1364*log(x - 1/2)/16807 + 1364*log(x + 2/3)/1680
7

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GIAC/XCAS [A]  time = 0.207444, size = 81, normalized size = 1.25 \[ -\frac{242}{2401 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{36120}{2 \, x - 1} + \frac{40621}{{\left (2 \, x - 1\right )}^{2}} + 8031\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{1364}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")

[Out]

-242/2401/(2*x - 1) + 2/16807*(36120/(2*x - 1) + 40621/(2*x - 1)^2 + 8031)/(7/(2
*x - 1) + 3)^3 + 1364/16807*ln(abs(-7/(2*x - 1) - 3))