3.1448 \(\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^6} \, dx\)

Optimal. Leaf size=76 \[ -\frac{484}{16807 (3 x+2)}-\frac{121}{2401 (3 x+2)^2}-\frac{121}{1029 (3 x+2)^3}+\frac{17}{441 (3 x+2)^4}-\frac{1}{315 (3 x+2)^5}-\frac{968 \log (1-2 x)}{117649}+\frac{968 \log (3 x+2)}{117649} \]

[Out]

-1/(315*(2 + 3*x)^5) + 17/(441*(2 + 3*x)^4) - 121/(1029*(2 + 3*x)^3) - 121/(2401
*(2 + 3*x)^2) - 484/(16807*(2 + 3*x)) - (968*Log[1 - 2*x])/117649 + (968*Log[2 +
3*x])/117649

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Rubi [A]  time = 0.0769572, antiderivative size = 76, 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 \[ -\frac{484}{16807 (3 x+2)}-\frac{121}{2401 (3 x+2)^2}-\frac{121}{1029 (3 x+2)^3}+\frac{17}{441 (3 x+2)^4}-\frac{1}{315 (3 x+2)^5}-\frac{968 \log (1-2 x)}{117649}+\frac{968 \log (3 x+2)}{117649} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^6),x]

[Out]

-1/(315*(2 + 3*x)^5) + 17/(441*(2 + 3*x)^4) - 121/(1029*(2 + 3*x)^3) - 121/(2401
*(2 + 3*x)^2) - 484/(16807*(2 + 3*x)) - (968*Log[1 - 2*x])/117649 + (968*Log[2 +
3*x])/117649

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Rubi in Sympy [A]  time = 11.4214, size = 66, normalized size = 0.87 \[ - \frac{968 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{968 \log{\left (3 x + 2 \right )}}{117649} - \frac{484}{16807 \left (3 x + 2\right )} - \frac{121}{2401 \left (3 x + 2\right )^{2}} - \frac{121}{1029 \left (3 x + 2\right )^{3}} + \frac{17}{441 \left (3 x + 2\right )^{4}} - \frac{1}{315 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**2/(1-2*x)/(2+3*x)**6,x)

[Out]

-968*log(-2*x + 1)/117649 + 968*log(3*x + 2)/117649 - 484/(16807*(3*x + 2)) - 12
1/(2401*(3*x + 2)**2) - 121/(1029*(3*x + 2)**3) + 17/(441*(3*x + 2)**4) - 1/(315
*(3*x + 2)**5)

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Mathematica [A]  time = 0.0758398, size = 52, normalized size = 0.68 \[ \frac{4 \left (-\frac{7 \left (1764180 x^4+5733585 x^3+7563105 x^2+4442775 x+953231\right )}{4 (3 x+2)^5}-10890 \log (1-2 x)+10890 \log (6 x+4)\right )}{5294205} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^6),x]

[Out]

(4*((-7*(953231 + 4442775*x + 7563105*x^2 + 5733585*x^3 + 1764180*x^4))/(4*(2 +
3*x)^5) - 10890*Log[1 - 2*x] + 10890*Log[4 + 6*x]))/5294205

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Maple [A]  time = 0.013, size = 63, normalized size = 0.8 \[ -{\frac{1}{315\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{17}{441\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{121}{1029\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{121}{2401\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{484}{33614+50421\,x}}+{\frac{968\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{968\,\ln \left ( -1+2\,x \right ) }{117649}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)/(2+3*x)^6,x)

[Out]

-1/315/(2+3*x)^5+17/441/(2+3*x)^4-121/1029/(2+3*x)^3-121/2401/(2+3*x)^2-484/1680
7/(2+3*x)+968/117649*ln(2+3*x)-968/117649*ln(-1+2*x)

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Maxima [A]  time = 1.34183, size = 89, normalized size = 1.17 \[ -\frac{1764180 \, x^{4} + 5733585 \, x^{3} + 7563105 \, x^{2} + 4442775 \, x + 953231}{756315 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{968}{117649} \, \log \left (3 \, x + 2\right ) - \frac{968}{117649} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^6*(2*x - 1)),x, algorithm="maxima")

[Out]

-1/756315*(1764180*x^4 + 5733585*x^3 + 7563105*x^2 + 4442775*x + 953231)/(243*x^
5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32) + 968/117649*log(3*x + 2) - 968/1
17649*log(2*x - 1)

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Fricas [A]  time = 0.214574, size = 155, normalized size = 2.04 \[ -\frac{12349260 \, x^{4} + 40135095 \, x^{3} + 52941735 \, x^{2} - 43560 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 43560 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 31099425 \, x + 6672617}{5294205 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^6*(2*x - 1)),x, algorithm="fricas")

[Out]

-1/5294205*(12349260*x^4 + 40135095*x^3 + 52941735*x^2 - 43560*(243*x^5 + 810*x^
4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 43560*(243*x^5 + 810*x^4 + 1
080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 31099425*x + 6672617)/(243*x^5 +
810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [A]  time = 0.529569, size = 65, normalized size = 0.86 \[ - \frac{1764180 x^{4} + 5733585 x^{3} + 7563105 x^{2} + 4442775 x + 953231}{183784545 x^{5} + 612615150 x^{4} + 816820200 x^{3} + 544546800 x^{2} + 181515600 x + 24202080} - \frac{968 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{968 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x)/(2+3*x)**6,x)

[Out]

-(1764180*x**4 + 5733585*x**3 + 7563105*x**2 + 4442775*x + 953231)/(183784545*x*
*5 + 612615150*x**4 + 816820200*x**3 + 544546800*x**2 + 181515600*x + 24202080)
- 968*log(x - 1/2)/117649 + 968*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.211624, size = 65, normalized size = 0.86 \[ -\frac{1764180 \, x^{4} + 5733585 \, x^{3} + 7563105 \, x^{2} + 4442775 \, x + 953231}{756315 \,{\left (3 \, x + 2\right )}^{5}} + \frac{968}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{968}{117649} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^6*(2*x - 1)),x, algorithm="giac")

[Out]

-1/756315*(1764180*x^4 + 5733585*x^3 + 7563105*x^2 + 4442775*x + 953231)/(3*x +
2)^5 + 968/117649*ln(abs(3*x + 2)) - 968/117649*ln(abs(2*x - 1))