3.1532 \(\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{22}{343 (1-2 x)}-\frac{31}{343 (3 x+2)}+\frac{1}{98 (3 x+2)^2}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (3 x+2)}{2401} \]

[Out]

22/(343*(1 - 2*x)) + 1/(98*(2 + 3*x)^2) - 31/(343*(2 + 3*x)) - (128*Log[1 - 2*x]
)/2401 + (128*Log[2 + 3*x])/2401

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Rubi [A]  time = 0.0571109, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{22}{343 (1-2 x)}-\frac{31}{343 (3 x+2)}+\frac{1}{98 (3 x+2)^2}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (3 x+2)}{2401} \]

Antiderivative was successfully verified.

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

[Out]

22/(343*(1 - 2*x)) + 1/(98*(2 + 3*x)^2) - 31/(343*(2 + 3*x)) - (128*Log[1 - 2*x]
)/2401 + (128*Log[2 + 3*x])/2401

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Rubi in Sympy [A]  time = 8.51392, size = 42, normalized size = 0.78 \[ - \frac{128 \log{\left (- 2 x + 1 \right )}}{2401} + \frac{128 \log{\left (3 x + 2 \right )}}{2401} - \frac{31}{343 \left (3 x + 2\right )} + \frac{1}{98 \left (3 x + 2\right )^{2}} + \frac{22}{343 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-128*log(-2*x + 1)/2401 + 128*log(3*x + 2)/2401 - 31/(343*(3*x + 2)) + 1/(98*(3*
x + 2)**2) + 22/(343*(-2*x + 1))

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Mathematica [A]  time = 0.0431718, size = 47, normalized size = 0.87 \[ \frac{-\frac{7 \left (768 x^2+576 x+59\right )}{(2 x-1) (3 x+2)^2}-256 \log (1-2 x)+256 \log (6 x+4)}{4802} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(59 + 576*x + 768*x^2))/((-1 + 2*x)*(2 + 3*x)^2) - 256*Log[1 - 2*x] + 256*L
og[4 + 6*x])/4802

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Maple [A]  time = 0.014, size = 45, normalized size = 0.8 \[{\frac{1}{98\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{31}{686+1029\,x}}+{\frac{128\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{22}{-343+686\,x}}-{\frac{128\,\ln \left ( -1+2\,x \right ) }{2401}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/98/(2+3*x)^2-31/343/(2+3*x)+128/2401*ln(2+3*x)-22/343/(-1+2*x)-128/2401*ln(-1+
2*x)

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Maxima [A]  time = 1.32745, size = 62, normalized size = 1.15 \[ -\frac{768 \, x^{2} + 576 \, x + 59}{686 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac{128}{2401} \, \log \left (3 \, x + 2\right ) - \frac{128}{2401} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/686*(768*x^2 + 576*x + 59)/(18*x^3 + 15*x^2 - 4*x - 4) + 128/2401*log(3*x + 2
) - 128/2401*log(2*x - 1)

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Fricas [A]  time = 0.216017, size = 101, normalized size = 1.87 \[ -\frac{5376 \, x^{2} - 256 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) + 256 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 4032 \, x + 413}{4802 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4802*(5376*x^2 - 256*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) + 256*(18*x^3 +
15*x^2 - 4*x - 4)*log(2*x - 1) + 4032*x + 413)/(18*x^3 + 15*x^2 - 4*x - 4)

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Sympy [A]  time = 0.361631, size = 44, normalized size = 0.81 \[ - \frac{768 x^{2} + 576 x + 59}{12348 x^{3} + 10290 x^{2} - 2744 x - 2744} - \frac{128 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{128 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(768*x**2 + 576*x + 59)/(12348*x**3 + 10290*x**2 - 2744*x - 2744) - 128*log(x -
1/2)/2401 + 128*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.208832, size = 69, normalized size = 1.28 \[ -\frac{22}{343 \,{\left (2 \, x - 1\right )}} + \frac{6 \,{\left (\frac{203}{2 \, x - 1} + 90\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} + \frac{128}{2401} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-22/343/(2*x - 1) + 6/2401*(203/(2*x - 1) + 90)/(7/(2*x - 1) + 3)^2 + 128/2401*l
n(abs(-7/(2*x - 1) - 3))