3.1624 \(\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{128}{2401 (1-2 x)}-\frac{87}{2401 (3 x+2)}+\frac{11}{343 (1-2 x)^2}+\frac{3}{686 (3 x+2)^2}-\frac{558 \log (1-2 x)}{16807}+\frac{558 \log (3 x+2)}{16807} \]

[Out]

11/(343*(1 - 2*x)^2) + 128/(2401*(1 - 2*x)) + 3/(686*(2 + 3*x)^2) - 87/(2401*(2
+ 3*x)) - (558*Log[1 - 2*x])/16807 + (558*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0683202, 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 \[ \frac{128}{2401 (1-2 x)}-\frac{87}{2401 (3 x+2)}+\frac{11}{343 (1-2 x)^2}+\frac{3}{686 (3 x+2)^2}-\frac{558 \log (1-2 x)}{16807}+\frac{558 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

11/(343*(1 - 2*x)^2) + 128/(2401*(1 - 2*x)) + 3/(686*(2 + 3*x)^2) - 87/(2401*(2
+ 3*x)) - (558*Log[1 - 2*x])/16807 + (558*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 9.8307, size = 53, normalized size = 0.82 \[ - \frac{558 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{558 \log{\left (3 x + 2 \right )}}{16807} - \frac{87}{2401 \left (3 x + 2\right )} + \frac{3}{686 \left (3 x + 2\right )^{2}} + \frac{128}{2401 \left (- 2 x + 1\right )} + \frac{11}{343 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-558*log(-2*x + 1)/16807 + 558*log(3*x + 2)/16807 - 87/(2401*(3*x + 2)) + 3/(686
*(3*x + 2)**2) + 128/(2401*(-2*x + 1)) + 11/(343*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0446088, size = 48, normalized size = 0.74 \[ \frac{\frac{7 \left (-6696 x^3-1674 x^2+3658 x+1313\right )}{\left (6 x^2+x-2\right )^2}-1116 \log (1-2 x)+1116 \log (3 x+2)}{33614} \]

Antiderivative was successfully verified.

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

[Out]

((7*(1313 + 3658*x - 1674*x^2 - 6696*x^3))/(-2 + x + 6*x^2)^2 - 1116*Log[1 - 2*x
] + 1116*Log[2 + 3*x])/33614

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Maple [A]  time = 0.014, size = 54, normalized size = 0.8 \[{\frac{3}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{87}{4802+7203\,x}}+{\frac{558\,\ln \left ( 2+3\,x \right ) }{16807}}+{\frac{11}{343\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{128}{-2401+4802\,x}}-{\frac{558\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/686/(2+3*x)^2-87/2401/(2+3*x)+558/16807*ln(2+3*x)+11/343/(-1+2*x)^2-128/2401/(
-1+2*x)-558/16807*ln(-1+2*x)

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Maxima [A]  time = 1.34067, size = 76, normalized size = 1.17 \[ -\frac{6696 \, x^{3} + 1674 \, x^{2} - 3658 \, x - 1313}{4802 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac{558}{16807} \, \log \left (3 \, x + 2\right ) - \frac{558}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4802*(6696*x^3 + 1674*x^2 - 3658*x - 1313)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x +
4) + 558/16807*log(3*x + 2) - 558/16807*log(2*x - 1)

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Fricas [A]  time = 0.204938, size = 128, normalized size = 1.97 \[ -\frac{46872 \, x^{3} + 11718 \, x^{2} - 1116 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 1116 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 25606 \, x - 9191}{33614 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/33614*(46872*x^3 + 11718*x^2 - 1116*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(
3*x + 2) + 1116*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 25606*x - 91
91)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)

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Sympy [A]  time = 0.435352, size = 54, normalized size = 0.83 \[ - \frac{6696 x^{3} + 1674 x^{2} - 3658 x - 1313}{172872 x^{4} + 57624 x^{3} - 110446 x^{2} - 19208 x + 19208} - \frac{558 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{558 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(6696*x**3 + 1674*x**2 - 3658*x - 1313)/(172872*x**4 + 57624*x**3 - 110446*x**2
- 19208*x + 19208) - 558*log(x - 1/2)/16807 + 558*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.210616, size = 62, normalized size = 0.95 \[ -\frac{6696 \, x^{3} + 1674 \, x^{2} - 3658 \, x - 1313}{4802 \,{\left (6 \, x^{2} + x - 2\right )}^{2}} + \frac{558}{16807} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{558}{16807} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4802*(6696*x^3 + 1674*x^2 - 3658*x - 1313)/(6*x^2 + x - 2)^2 + 558/16807*ln(a
bs(3*x + 2)) - 558/16807*ln(abs(2*x - 1))