3.2393 \(\int \frac{5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx\)

Optimal. Leaf size=77 \[ -\frac{3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac{2618}{125 (2 x+3)}-\frac{428}{25 (2 x+3)^2}-\log (x+1)+\frac{8104}{625} \log (2 x+3)-\frac{7479}{625} \log (3 x+2) \]

[Out]

-428/(25*(3 + 2*x)^2) - 2618/(125*(3 + 2*x)) - (3*(37 + 47*x))/(5*(3 + 2*x)^2*(2
+ 5*x + 3*x^2)) - Log[1 + x] + (8104*Log[3 + 2*x])/625 - (7479*Log[2 + 3*x])/62
5

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Rubi [A]  time = 0.116576, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac{2618}{125 (2 x+3)}-\frac{428}{25 (2 x+3)^2}-\log (x+1)+\frac{8104}{625} \log (2 x+3)-\frac{7479}{625} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

-428/(25*(3 + 2*x)^2) - 2618/(125*(3 + 2*x)) - (3*(37 + 47*x))/(5*(3 + 2*x)^2*(2
+ 5*x + 3*x^2)) - Log[1 + x] + (8104*Log[3 + 2*x])/625 - (7479*Log[2 + 3*x])/62
5

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Rubi in Sympy [A]  time = 22.5861, size = 65, normalized size = 0.84 \[ - \log{\left (x + 1 \right )} + \frac{8104 \log{\left (2 x + 3 \right )}}{625} - \frac{7479 \log{\left (3 x + 2 \right )}}{625} - \frac{2618}{125 \left (2 x + 3\right )} - \frac{141 x + 111}{5 \left (2 x + 3\right )^{2} \left (3 x^{2} + 5 x + 2\right )} - \frac{428}{25 \left (2 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-log(x + 1) + 8104*log(2*x + 3)/625 - 7479*log(3*x + 2)/625 - 2618/(125*(2*x + 3
)) - (141*x + 111)/(5*(2*x + 3)**2*(3*x**2 + 5*x + 2)) - 428/(25*(2*x + 3)**2)

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Mathematica [A]  time = 0.056932, size = 66, normalized size = 0.86 \[ \frac{1}{625} \left (-\frac{15 (903 x+653)}{3 x^2+5 x+2}-\frac{4060}{2 x+3}-\frac{650}{(2 x+3)^2}-7479 \log (-6 x-4)-625 \log (-2 (x+1))+8104 \log (2 x+3)\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-650/(3 + 2*x)^2 - 4060/(3 + 2*x) - (15*(653 + 903*x))/(2 + 5*x + 3*x^2) - 7479
*Log[-4 - 6*x] - 625*Log[-2*(1 + x)] + 8104*Log[3 + 2*x])/625

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Maple [A]  time = 0.018, size = 58, normalized size = 0.8 \[ -{\frac{459}{250+375\,x}}-{\frac{7479\,\ln \left ( 2+3\,x \right ) }{625}}-{\frac{26}{25\, \left ( 3+2\,x \right ) ^{2}}}-{\frac{812}{375+250\,x}}+{\frac{8104\,\ln \left ( 3+2\,x \right ) }{625}}-6\, \left ( 1+x \right ) ^{-1}-\ln \left ( 1+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-459/125/(2+3*x)-7479/625*ln(2+3*x)-26/25/(3+2*x)^2-812/125/(3+2*x)+8104/625*ln(
3+2*x)-6/(1+x)-ln(1+x)

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Maxima [A]  time = 0.68647, size = 84, normalized size = 1.09 \[ -\frac{15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \,{\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} - \frac{7479}{625} \, \log \left (3 \, x + 2\right ) + \frac{8104}{625} \, \log \left (2 \, x + 3\right ) - \log \left (x + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/125*(15708*x^3 + 56162*x^2 + 63967*x + 22763)/(12*x^4 + 56*x^3 + 95*x^2 + 69*
x + 18) - 7479/625*log(3*x + 2) + 8104/625*log(2*x + 3) - log(x + 1)

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Fricas [A]  time = 0.266386, size = 163, normalized size = 2.12 \[ -\frac{78540 \, x^{3} + 280810 \, x^{2} + 7479 \,{\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 8104 \,{\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (2 \, x + 3\right ) + 625 \,{\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (x + 1\right ) + 319835 \, x + 113815}{625 \,{\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/625*(78540*x^3 + 280810*x^2 + 7479*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log
(3*x + 2) - 8104*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(2*x + 3) + 625*(12*x
^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(x + 1) + 319835*x + 113815)/(12*x^4 + 56*x
^3 + 95*x^2 + 69*x + 18)

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Sympy [A]  time = 0.600857, size = 60, normalized size = 0.78 \[ - \frac{15708 x^{3} + 56162 x^{2} + 63967 x + 22763}{1500 x^{4} + 7000 x^{3} + 11875 x^{2} + 8625 x + 2250} - \frac{7479 \log{\left (x + \frac{2}{3} \right )}}{625} - \log{\left (x + 1 \right )} + \frac{8104 \log{\left (x + \frac{3}{2} \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(15708*x**3 + 56162*x**2 + 63967*x + 22763)/(1500*x**4 + 7000*x**3 + 11875*x**2
+ 8625*x + 2250) - 7479*log(x + 2/3)/625 - log(x + 1) + 8104*log(x + 3/2)/625

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GIAC/XCAS [A]  time = 0.28049, size = 84, normalized size = 1.09 \[ -\frac{15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \,{\left (3 \, x + 2\right )}{\left (2 \, x + 3\right )}^{2}{\left (x + 1\right )}} - \frac{7479}{625} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{8104}{625} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) -{\rm ln}\left ({\left | x + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/125*(15708*x^3 + 56162*x^2 + 63967*x + 22763)/((3*x + 2)*(2*x + 3)^2*(x + 1))
- 7479/625*ln(abs(3*x + 2)) + 8104/625*ln(abs(2*x + 3)) - ln(abs(x + 1))