3.1637 \(\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^2} \, dx\)

Optimal. Leaf size=54 \[ -\frac{22}{343 (1-2 x)}-\frac{1}{343 (3 x+2)}+\frac{121}{196 (1-2 x)^2}+\frac{64 \log (1-2 x)}{2401}-\frac{64 \log (3 x+2)}{2401} \]

[Out]

121/(196*(1 - 2*x)^2) - 22/(343*(1 - 2*x)) - 1/(343*(2 + 3*x)) + (64*Log[1 - 2*x
])/2401 - (64*Log[2 + 3*x])/2401

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Rubi [A]  time = 0.0624469, antiderivative size = 54, 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 \[ -\frac{22}{343 (1-2 x)}-\frac{1}{343 (3 x+2)}+\frac{121}{196 (1-2 x)^2}+\frac{64 \log (1-2 x)}{2401}-\frac{64 \log (3 x+2)}{2401} \]

Antiderivative was successfully verified.

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

[Out]

121/(196*(1 - 2*x)^2) - 22/(343*(1 - 2*x)) - 1/(343*(2 + 3*x)) + (64*Log[1 - 2*x
])/2401 - (64*Log[2 + 3*x])/2401

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Rubi in Sympy [A]  time = 8.98724, size = 42, normalized size = 0.78 \[ \frac{64 \log{\left (- 2 x + 1 \right )}}{2401} - \frac{64 \log{\left (3 x + 2 \right )}}{2401} - \frac{1}{343 \left (3 x + 2\right )} - \frac{22}{343 \left (- 2 x + 1\right )} + \frac{121}{196 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64*log(-2*x + 1)/2401 - 64*log(3*x + 2)/2401 - 1/(343*(3*x + 2)) - 22/(343*(-2*x
+ 1)) + 121/(196*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0589354, size = 47, normalized size = 0.87 \[ \frac{\frac{7 \left (512 x^2+2645 x+1514\right )}{(1-2 x)^2 (3 x+2)}+256 \log (1-2 x)-256 \log (6 x+4)}{9604} \]

Antiderivative was successfully verified.

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

[Out]

((7*(1514 + 2645*x + 512*x^2))/((1 - 2*x)^2*(2 + 3*x)) + 256*Log[1 - 2*x] - 256*
Log[4 + 6*x])/9604

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Maple [A]  time = 0.013, size = 45, normalized size = 0.8 \[ -{\frac{1}{686+1029\,x}}-{\frac{64\,\ln \left ( 2+3\,x \right ) }{2401}}+{\frac{121}{196\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{22}{-343+686\,x}}+{\frac{64\,\ln \left ( -1+2\,x \right ) }{2401}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/343/(2+3*x)-64/2401*ln(2+3*x)+121/196/(-1+2*x)^2+22/343/(-1+2*x)+64/2401*ln(-
1+2*x)

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Maxima [A]  time = 1.32623, size = 62, normalized size = 1.15 \[ \frac{512 \, x^{2} + 2645 \, x + 1514}{1372 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} - \frac{64}{2401} \, \log \left (3 \, x + 2\right ) + \frac{64}{2401} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1372*(512*x^2 + 2645*x + 1514)/(12*x^3 - 4*x^2 - 5*x + 2) - 64/2401*log(3*x +
2) + 64/2401*log(2*x - 1)

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Fricas [A]  time = 0.222797, size = 101, normalized size = 1.87 \[ \frac{3584 \, x^{2} - 256 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 256 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 18515 \, x + 10598}{9604 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9604*(3584*x^2 - 256*(12*x^3 - 4*x^2 - 5*x + 2)*log(3*x + 2) + 256*(12*x^3 - 4
*x^2 - 5*x + 2)*log(2*x - 1) + 18515*x + 10598)/(12*x^3 - 4*x^2 - 5*x + 2)

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Sympy [A]  time = 0.41949, size = 44, normalized size = 0.81 \[ \frac{512 x^{2} + 2645 x + 1514}{16464 x^{3} - 5488 x^{2} - 6860 x + 2744} + \frac{64 \log{\left (x - \frac{1}{2} \right )}}{2401} - \frac{64 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(512*x**2 + 2645*x + 1514)/(16464*x**3 - 5488*x**2 - 6860*x + 2744) + 64*log(x -
1/2)/2401 - 64*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.210036, size = 69, normalized size = 1.28 \[ -\frac{1}{343 \,{\left (3 \, x + 2\right )}} + \frac{33 \,{\left (\frac{203}{3 \, x + 2} - 25\right )}}{2401 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} + \frac{64}{2401} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/343/(3*x + 2) + 33/2401*(203/(3*x + 2) - 25)/(7/(3*x + 2) - 2)^2 + 64/2401*ln
(abs(-7/(3*x + 2) + 2))