3.1533 \(\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^4} \, dx\)

Optimal. Leaf size=65 \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]

[Out]

44/(2401*(1 - 2*x)) + 1/(147*(2 + 3*x)^3) - 31/(686*(2 + 3*x)^2) - 128/(2401*(2
+ 3*x)) - (388*Log[1 - 2*x])/16807 + (388*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0707719, antiderivative size = 65, 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 \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

44/(2401*(1 - 2*x)) + 1/(147*(2 + 3*x)^3) - 31/(686*(2 + 3*x)^2) - 128/(2401*(2
+ 3*x)) - (388*Log[1 - 2*x])/16807 + (388*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 9.79685, size = 53, normalized size = 0.82 \[ - \frac{388 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{388 \log{\left (3 x + 2 \right )}}{16807} - \frac{128}{2401 \left (3 x + 2\right )} - \frac{31}{686 \left (3 x + 2\right )^{2}} + \frac{1}{147 \left (3 x + 2\right )^{3}} + \frac{44}{2401 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-388*log(-2*x + 1)/16807 + 388*log(3*x + 2)/16807 - 128/(2401*(3*x + 2)) - 31/(6
86*(3*x + 2)**2) + 1/(147*(3*x + 2)**3) + 44/(2401*(-2*x + 1))

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Mathematica [A]  time = 0.0525716, size = 52, normalized size = 0.8 \[ \frac{-\frac{7 \left (20952 x^3+29682 x^2+6887 x-2164\right )}{(2 x-1) (3 x+2)^3}-2328 \log (3-6 x)+2328 \log (3 x+2)}{100842} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(-2164 + 6887*x + 29682*x^2 + 20952*x^3))/((-1 + 2*x)*(2 + 3*x)^3) - 2328*L
og[3 - 6*x] + 2328*Log[2 + 3*x])/100842

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Maple [A]  time = 0.016, size = 54, normalized size = 0.8 \[{\frac{1}{147\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{31}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{128}{4802+7203\,x}}+{\frac{388\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{44}{-2401+4802\,x}}-{\frac{388\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/147/(2+3*x)^3-31/686/(2+3*x)^2-128/2401/(2+3*x)+388/16807*ln(2+3*x)-44/2401/(-
1+2*x)-388/16807*ln(-1+2*x)

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Maxima [A]  time = 1.34258, size = 76, normalized size = 1.17 \[ -\frac{20952 \, x^{3} + 29682 \, x^{2} + 6887 \, x - 2164}{14406 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{388}{16807} \, \log \left (3 \, x + 2\right ) - \frac{388}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/14406*(20952*x^3 + 29682*x^2 + 6887*x - 2164)/(54*x^4 + 81*x^3 + 18*x^2 - 20*
x - 8) + 388/16807*log(3*x + 2) - 388/16807*log(2*x - 1)

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Fricas [A]  time = 0.208982, size = 128, normalized size = 1.97 \[ -\frac{146664 \, x^{3} + 207774 \, x^{2} - 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 48209 \, x - 15148}{100842 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/100842*(146664*x^3 + 207774*x^2 - 2328*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*
log(3*x + 2) + 2328*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) + 48209*x
- 15148)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)

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Sympy [A]  time = 0.407502, size = 54, normalized size = 0.83 \[ - \frac{20952 x^{3} + 29682 x^{2} + 6887 x - 2164}{777924 x^{4} + 1166886 x^{3} + 259308 x^{2} - 288120 x - 115248} - \frac{388 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{388 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(20952*x**3 + 29682*x**2 + 6887*x - 2164)/(777924*x**4 + 1166886*x**3 + 259308*
x**2 - 288120*x - 115248) - 388*log(x - 1/2)/16807 + 388*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.206064, size = 81, normalized size = 1.25 \[ -\frac{44}{2401 \,{\left (2 \, x - 1\right )}} + \frac{18 \,{\left (\frac{2415}{2 \, x - 1} + \frac{3038}{{\left (2 \, x - 1\right )}^{2}} + 473\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{388}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-44/2401/(2*x - 1) + 18/16807*(2415/(2*x - 1) + 3038/(2*x - 1)^2 + 473)/(7/(2*x
- 1) + 3)^3 + 388/16807*ln(abs(-7/(2*x - 1) - 3))