3.1638 \(\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{319}{2401 (1-2 x)}+\frac{64}{2401 (3 x+2)}+\frac{121}{686 (1-2 x)^2}-\frac{1}{686 (3 x+2)^2}-\frac{829 \log (1-2 x)}{16807}+\frac{829 \log (3 x+2)}{16807} \]

[Out]

121/(686*(1 - 2*x)^2) + 319/(2401*(1 - 2*x)) - 1/(686*(2 + 3*x)^2) + 64/(2401*(2
+ 3*x)) - (829*Log[1 - 2*x])/16807 + (829*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0752056, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{319}{2401 (1-2 x)}+\frac{64}{2401 (3 x+2)}+\frac{121}{686 (1-2 x)^2}-\frac{1}{686 (3 x+2)^2}-\frac{829 \log (1-2 x)}{16807}+\frac{829 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

121/(686*(1 - 2*x)^2) + 319/(2401*(1 - 2*x)) - 1/(686*(2 + 3*x)^2) + 64/(2401*(2
+ 3*x)) - (829*Log[1 - 2*x])/16807 + (829*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 10.2591, size = 53, normalized size = 0.82 \[ - \frac{829 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{829 \log{\left (3 x + 2 \right )}}{16807} + \frac{64}{2401 \left (3 x + 2\right )} - \frac{1}{686 \left (3 x + 2\right )^{2}} + \frac{319}{2401 \left (- 2 x + 1\right )} + \frac{121}{686 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-829*log(-2*x + 1)/16807 + 829*log(3*x + 2)/16807 + 64/(2401*(3*x + 2)) - 1/(686
*(3*x + 2)**2) + 319/(2401*(-2*x + 1)) + 121/(686*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0513176, size = 48, normalized size = 0.74 \[ \frac{-\frac{7 \left (9948 x^3+2487 x^2-12104 x-6189\right )}{\left (6 x^2+x-2\right )^2}-1658 \log (1-2 x)+1658 \log (3 x+2)}{33614} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(-6189 - 12104*x + 2487*x^2 + 9948*x^3))/(-2 + x + 6*x^2)^2 - 1658*Log[1 -
2*x] + 1658*Log[2 + 3*x])/33614

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Maple [A]  time = 0.016, size = 54, normalized size = 0.8 \[ -{\frac{1}{686\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{64}{4802+7203\,x}}+{\frac{829\,\ln \left ( 2+3\,x \right ) }{16807}}+{\frac{121}{686\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{319}{-2401+4802\,x}}-{\frac{829\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/686/(2+3*x)^2+64/2401/(2+3*x)+829/16807*ln(2+3*x)+121/686/(-1+2*x)^2-319/2401
/(-1+2*x)-829/16807*ln(-1+2*x)

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Maxima [A]  time = 1.33987, size = 76, normalized size = 1.17 \[ -\frac{9948 \, x^{3} + 2487 \, x^{2} - 12104 \, x - 6189}{4802 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac{829}{16807} \, \log \left (3 \, x + 2\right ) - \frac{829}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4802*(9948*x^3 + 2487*x^2 - 12104*x - 6189)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x +
4) + 829/16807*log(3*x + 2) - 829/16807*log(2*x - 1)

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Fricas [A]  time = 0.211189, size = 128, normalized size = 1.97 \[ -\frac{69636 \, x^{3} + 17409 \, x^{2} - 1658 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 1658 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 84728 \, x - 43323}{33614 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/33614*(69636*x^3 + 17409*x^2 - 1658*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(
3*x + 2) + 1658*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 84728*x - 43
323)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)

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Sympy [A]  time = 0.446493, size = 54, normalized size = 0.83 \[ - \frac{9948 x^{3} + 2487 x^{2} - 12104 x - 6189}{172872 x^{4} + 57624 x^{3} - 110446 x^{2} - 19208 x + 19208} - \frac{829 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{829 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(9948*x**3 + 2487*x**2 - 12104*x - 6189)/(172872*x**4 + 57624*x**3 - 110446*x**
2 - 19208*x + 19208) - 829*log(x - 1/2)/16807 + 829*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.210005, size = 62, normalized size = 0.95 \[ -\frac{9948 \, x^{3} + 2487 \, x^{2} - 12104 \, x - 6189}{4802 \,{\left (6 \, x^{2} + x - 2\right )}^{2}} + \frac{829}{16807} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{829}{16807} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4802*(9948*x^3 + 2487*x^2 - 12104*x - 6189)/(6*x^2 + x - 2)^2 + 829/16807*ln(
abs(3*x + 2)) - 829/16807*ln(abs(2*x - 1))