3.1567 \(\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^5} \, dx\)

Optimal. Leaf size=76 \[ \frac{2662}{16807 (1-2 x)}-\frac{3267}{16807 (3 x+2)}+\frac{363}{4802 (3 x+2)^2}-\frac{101}{9261 (3 x+2)^3}+\frac{1}{1764 (3 x+2)^4}-\frac{14520 \log (1-2 x)}{117649}+\frac{14520 \log (3 x+2)}{117649} \]

[Out]

2662/(16807*(1 - 2*x)) + 1/(1764*(2 + 3*x)^4) - 101/(9261*(2 + 3*x)^3) + 363/(48
02*(2 + 3*x)^2) - 3267/(16807*(2 + 3*x)) - (14520*Log[1 - 2*x])/117649 + (14520*
Log[2 + 3*x])/117649

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Rubi [A]  time = 0.0892964, 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 \[ \frac{2662}{16807 (1-2 x)}-\frac{3267}{16807 (3 x+2)}+\frac{363}{4802 (3 x+2)^2}-\frac{101}{9261 (3 x+2)^3}+\frac{1}{1764 (3 x+2)^4}-\frac{14520 \log (1-2 x)}{117649}+\frac{14520 \log (3 x+2)}{117649} \]

Antiderivative was successfully verified.

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

[Out]

2662/(16807*(1 - 2*x)) + 1/(1764*(2 + 3*x)^4) - 101/(9261*(2 + 3*x)^3) + 363/(48
02*(2 + 3*x)^2) - 3267/(16807*(2 + 3*x)) - (14520*Log[1 - 2*x])/117649 + (14520*
Log[2 + 3*x])/117649

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Rubi in Sympy [A]  time = 11.532, size = 63, normalized size = 0.83 \[ - \frac{14520 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{14520 \log{\left (3 x + 2 \right )}}{117649} - \frac{3267}{16807 \left (3 x + 2\right )} + \frac{363}{4802 \left (3 x + 2\right )^{2}} - \frac{101}{9261 \left (3 x + 2\right )^{3}} + \frac{1}{1764 \left (3 x + 2\right )^{4}} + \frac{2662}{16807 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-14520*log(-2*x + 1)/117649 + 14520*log(3*x + 2)/117649 - 3267/(16807*(3*x + 2))
+ 363/(4802*(3*x + 2)**2) - 101/(9261*(3*x + 2)**3) + 1/(1764*(3*x + 2)**4) + 2
662/(16807*(-2*x + 1))

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Mathematica [A]  time = 0.0790009, size = 59, normalized size = 0.78 \[ \frac{2 \left (-\frac{7 \left (42340320 x^4+88209000 x^3+66510750 x^2+21109490 x+2287541\right )}{8 (2 x-1) (3 x+2)^4}-196020 \log (1-2 x)+196020 \log (6 x+4)\right )}{3176523} \]

Antiderivative was successfully verified.

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

[Out]

(2*((-7*(2287541 + 21109490*x + 66510750*x^2 + 88209000*x^3 + 42340320*x^4))/(8*
(-1 + 2*x)*(2 + 3*x)^4) - 196020*Log[1 - 2*x] + 196020*Log[4 + 6*x]))/3176523

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Maple [A]  time = 0.015, size = 63, normalized size = 0.8 \[{\frac{1}{1764\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{101}{9261\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{363}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{3267}{33614+50421\,x}}+{\frac{14520\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{2662}{-16807+33614\,x}}-{\frac{14520\,\ln \left ( -1+2\,x \right ) }{117649}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1764/(2+3*x)^4-101/9261/(2+3*x)^3+363/4802/(2+3*x)^2-3267/16807/(2+3*x)+14520/
117649*ln(2+3*x)-2662/16807/(-1+2*x)-14520/117649*ln(-1+2*x)

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Maxima [A]  time = 1.34879, size = 89, normalized size = 1.17 \[ -\frac{42340320 \, x^{4} + 88209000 \, x^{3} + 66510750 \, x^{2} + 21109490 \, x + 2287541}{1815156 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac{14520}{117649} \, \log \left (3 \, x + 2\right ) - \frac{14520}{117649} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1815156*(42340320*x^4 + 88209000*x^3 + 66510750*x^2 + 21109490*x + 2287541)/(
162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16) + 14520/117649*log(3*x + 2) -
14520/117649*log(2*x - 1)

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Fricas [A]  time = 0.225263, size = 155, normalized size = 2.04 \[ -\frac{296382240 \, x^{4} + 617463000 \, x^{3} + 465575250 \, x^{2} - 1568160 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) + 1568160 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) + 147766430 \, x + 16012787}{12706092 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12706092*(296382240*x^4 + 617463000*x^3 + 465575250*x^2 - 1568160*(162*x^5 +
351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(3*x + 2) + 1568160*(162*x^5 + 351*x^
4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(2*x - 1) + 147766430*x + 16012787)/(162*x^
5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)

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Sympy [A]  time = 0.485349, size = 65, normalized size = 0.86 \[ - \frac{42340320 x^{4} + 88209000 x^{3} + 66510750 x^{2} + 21109490 x + 2287541}{294055272 x^{5} + 637119756 x^{4} + 392073696 x^{3} - 43563744 x^{2} - 116169984 x - 29042496} - \frac{14520 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{14520 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(42340320*x**4 + 88209000*x**3 + 66510750*x**2 + 21109490*x + 2287541)/(2940552
72*x**5 + 637119756*x**4 + 392073696*x**3 - 43563744*x**2 - 116169984*x - 290424
96) - 14520*log(x - 1/2)/117649 + 14520*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.209252, size = 90, normalized size = 1.18 \[ -\frac{3267}{16807 \,{\left (3 \, x + 2\right )}} + \frac{15972}{117649 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} + \frac{363}{4802 \,{\left (3 \, x + 2\right )}^{2}} - \frac{101}{9261 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{1764 \,{\left (3 \, x + 2\right )}^{4}} - \frac{14520}{117649} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3267/16807/(3*x + 2) + 15972/117649/(7/(3*x + 2) - 2) + 363/4802/(3*x + 2)^2 -
101/9261/(3*x + 2)^3 + 1/1764/(3*x + 2)^4 - 14520/117649*ln(abs(-7/(3*x + 2) + 2
))