3.2385 \(\int \frac{5-x}{(3+2 x)^4 \left (2+5 x+3 x^2\right )} \, dx\)

Optimal. Leaf size=60 \[ -\frac{597}{125 (2 x+3)}-\frac{99}{50 (2 x+3)^2}-\frac{13}{15 (2 x+3)^3}-6 \log (x+1)+\frac{3291}{625} \log (2 x+3)+\frac{459}{625} \log (3 x+2) \]

[Out]

-13/(15*(3 + 2*x)^3) - 99/(50*(3 + 2*x)^2) - 597/(125*(3 + 2*x)) - 6*Log[1 + x]
+ (3291*Log[3 + 2*x])/625 + (459*Log[2 + 3*x])/625

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Rubi [A]  time = 0.0810543, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ -\frac{597}{125 (2 x+3)}-\frac{99}{50 (2 x+3)^2}-\frac{13}{15 (2 x+3)^3}-6 \log (x+1)+\frac{3291}{625} \log (2 x+3)+\frac{459}{625} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

-13/(15*(3 + 2*x)^3) - 99/(50*(3 + 2*x)^2) - 597/(125*(3 + 2*x)) - 6*Log[1 + x]
+ (3291*Log[3 + 2*x])/625 + (459*Log[2 + 3*x])/625

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Rubi in Sympy [A]  time = 15.5422, size = 53, normalized size = 0.88 \[ - 6 \log{\left (x + 1 \right )} + \frac{3291 \log{\left (2 x + 3 \right )}}{625} + \frac{459 \log{\left (3 x + 2 \right )}}{625} - \frac{597}{125 \left (2 x + 3\right )} - \frac{99}{50 \left (2 x + 3\right )^{2}} - \frac{13}{15 \left (2 x + 3\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6*log(x + 1) + 3291*log(2*x + 3)/625 + 459*log(3*x + 2)/625 - 597/(125*(2*x + 3
)) - 99/(50*(2*x + 3)**2) - 13/(15*(2*x + 3)**3)

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Mathematica [A]  time = 0.0487792, size = 62, normalized size = 1.03 \[ -\frac{597}{125 (2 x+3)}-\frac{99}{50 (2 x+3)^2}-\frac{13}{15 (2 x+3)^3}+\frac{459}{625} \log (-6 x-4)-6 \log (-2 (x+1))+\frac{3291}{625} \log (2 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-13/(15*(3 + 2*x)^3) - 99/(50*(3 + 2*x)^2) - 597/(125*(3 + 2*x)) + (459*Log[-4 -
6*x])/625 - 6*Log[-2*(1 + x)] + (3291*Log[3 + 2*x])/625

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Maple [A]  time = 0.013, size = 51, normalized size = 0.9 \[ -{\frac{13}{15\, \left ( 3+2\,x \right ) ^{3}}}-{\frac{99}{50\, \left ( 3+2\,x \right ) ^{2}}}-{\frac{597}{375+250\,x}}-6\,\ln \left ( 1+x \right ) +{\frac{3291\,\ln \left ( 3+2\,x \right ) }{625}}+{\frac{459\,\ln \left ( 2+3\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-13/15/(3+2*x)^3-99/50/(3+2*x)^2-597/125/(3+2*x)-6*ln(1+x)+3291/625*ln(3+2*x)+45
9/625*ln(2+3*x)

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Maxima [A]  time = 0.691796, size = 70, normalized size = 1.17 \[ -\frac{14328 \, x^{2} + 45954 \, x + 37343}{750 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} + \frac{459}{625} \, \log \left (3 \, x + 2\right ) + \frac{3291}{625} \, \log \left (2 \, x + 3\right ) - 6 \, \log \left (x + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/750*(14328*x^2 + 45954*x + 37343)/(8*x^3 + 36*x^2 + 54*x + 27) + 459/625*log(
3*x + 2) + 3291/625*log(2*x + 3) - 6*log(x + 1)

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Fricas [A]  time = 0.266309, size = 130, normalized size = 2.17 \[ -\frac{71640 \, x^{2} - 2754 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (3 \, x + 2\right ) - 19746 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (2 \, x + 3\right ) + 22500 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (x + 1\right ) + 229770 \, x + 186715}{3750 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3750*(71640*x^2 - 2754*(8*x^3 + 36*x^2 + 54*x + 27)*log(3*x + 2) - 19746*(8*x
^3 + 36*x^2 + 54*x + 27)*log(2*x + 3) + 22500*(8*x^3 + 36*x^2 + 54*x + 27)*log(x
+ 1) + 229770*x + 186715)/(8*x^3 + 36*x^2 + 54*x + 27)

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Sympy [A]  time = 0.543169, size = 51, normalized size = 0.85 \[ - \frac{14328 x^{2} + 45954 x + 37343}{6000 x^{3} + 27000 x^{2} + 40500 x + 20250} + \frac{459 \log{\left (x + \frac{2}{3} \right )}}{625} - 6 \log{\left (x + 1 \right )} + \frac{3291 \log{\left (x + \frac{3}{2} \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(14328*x**2 + 45954*x + 37343)/(6000*x**3 + 27000*x**2 + 40500*x + 20250) + 459
*log(x + 2/3)/625 - 6*log(x + 1) + 3291*log(x + 3/2)/625

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GIAC/XCAS [A]  time = 0.305975, size = 61, normalized size = 1.02 \[ -\frac{14328 \, x^{2} + 45954 \, x + 37343}{750 \,{\left (2 \, x + 3\right )}^{3}} + \frac{459}{625} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{3291}{625} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - 6 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/750*(14328*x^2 + 45954*x + 37343)/(2*x + 3)^3 + 459/625*ln(abs(3*x + 2)) + 32
91/625*ln(abs(2*x + 3)) - 6*ln(abs(x + 1))