3.1464 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx\)

Optimal. Leaf size=76 \[ -\frac{2662}{16807 (3 x+2)}-\frac{1331}{4802 (3 x+2)^2}+\frac{3469}{27783 (3 x+2)^3}-\frac{103}{5292 (3 x+2)^4}+\frac{1}{945 (3 x+2)^5}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (3 x+2)}{117649} \]

[Out]

1/(945*(2 + 3*x)^5) - 103/(5292*(2 + 3*x)^4) + 3469/(27783*(2 + 3*x)^3) - 1331/(
4802*(2 + 3*x)^2) - 2662/(16807*(2 + 3*x)) - (5324*Log[1 - 2*x])/117649 + (5324*
Log[2 + 3*x])/117649

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Rubi [A]  time = 0.077369, 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 \[ -\frac{2662}{16807 (3 x+2)}-\frac{1331}{4802 (3 x+2)^2}+\frac{3469}{27783 (3 x+2)^3}-\frac{103}{5292 (3 x+2)^4}+\frac{1}{945 (3 x+2)^5}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (3 x+2)}{117649} \]

Antiderivative was successfully verified.

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

[Out]

1/(945*(2 + 3*x)^5) - 103/(5292*(2 + 3*x)^4) + 3469/(27783*(2 + 3*x)^3) - 1331/(
4802*(2 + 3*x)^2) - 2662/(16807*(2 + 3*x)) - (5324*Log[1 - 2*x])/117649 + (5324*
Log[2 + 3*x])/117649

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Rubi in Sympy [A]  time = 11.5101, size = 66, normalized size = 0.87 \[ - \frac{5324 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{5324 \log{\left (3 x + 2 \right )}}{117649} - \frac{2662}{16807 \left (3 x + 2\right )} - \frac{1331}{4802 \left (3 x + 2\right )^{2}} + \frac{3469}{27783 \left (3 x + 2\right )^{3}} - \frac{103}{5292 \left (3 x + 2\right )^{4}} + \frac{1}{945 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5324*log(-2*x + 1)/117649 + 5324*log(3*x + 2)/117649 - 2662/(16807*(3*x + 2)) -
1331/(4802*(3*x + 2)**2) + 3469/(27783*(3*x + 2)**3) - 103/(5292*(3*x + 2)**4)
+ 1/(945*(3*x + 2)**5)

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Mathematica [A]  time = 0.0742322, size = 52, normalized size = 0.68 \[ \frac{2 \left (-\frac{7 \left (349307640 x^4+1135249830 x^3+1308416040 x^2+646472325 x+116805778\right )}{8 (3 x+2)^5}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right )}{47647845} \]

Antiderivative was successfully verified.

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

[Out]

(2*((-7*(116805778 + 646472325*x + 1308416040*x^2 + 1135249830*x^3 + 349307640*x
^4))/(8*(2 + 3*x)^5) - 1078110*Log[1 - 2*x] + 1078110*Log[4 + 6*x]))/47647845

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Maple [A]  time = 0.013, size = 63, normalized size = 0.8 \[{\frac{1}{945\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{103}{5292\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{3469}{27783\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1331}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2662}{33614+50421\,x}}+{\frac{5324\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{5324\,\ln \left ( -1+2\,x \right ) }{117649}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/945/(2+3*x)^5-103/5292/(2+3*x)^4+3469/27783/(2+3*x)^3-1331/4802/(2+3*x)^2-2662
/16807/(2+3*x)+5324/117649*ln(2+3*x)-5324/117649*ln(-1+2*x)

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Maxima [A]  time = 1.35185, size = 89, normalized size = 1.17 \[ -\frac{349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{5324}{117649} \, \log \left (3 \, x + 2\right ) - \frac{5324}{117649} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/27227340*(349307640*x^4 + 1135249830*x^3 + 1308416040*x^2 + 646472325*x + 116
805778)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32) + 5324/117649*log(
3*x + 2) - 5324/117649*log(2*x - 1)

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Fricas [A]  time = 0.212477, size = 155, normalized size = 2.04 \[ -\frac{2445153480 \, x^{4} + 7946748810 \, x^{3} + 9158912280 \, x^{2} - 8624880 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 8624880 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 4525306275 \, x + 817640446}{190591380 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/190591380*(2445153480*x^4 + 7946748810*x^3 + 9158912280*x^2 - 8624880*(243*x^
5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 8624880*(243*x^5 +
810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 4525306275*x + 817640
446)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [A]  time = 0.542211, size = 65, normalized size = 0.86 \[ - \frac{349307640 x^{4} + 1135249830 x^{3} + 1308416040 x^{2} + 646472325 x + 116805778}{6616243620 x^{5} + 22054145400 x^{4} + 29405527200 x^{3} + 19603684800 x^{2} + 6534561600 x + 871274880} - \frac{5324 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{5324 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(349307640*x**4 + 1135249830*x**3 + 1308416040*x**2 + 646472325*x + 116805778)/
(6616243620*x**5 + 22054145400*x**4 + 29405527200*x**3 + 19603684800*x**2 + 6534
561600*x + 871274880) - 5324*log(x - 1/2)/117649 + 5324*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.205374, size = 65, normalized size = 0.86 \[ -\frac{349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \,{\left (3 \, x + 2\right )}^{5}} + \frac{5324}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{5324}{117649} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/27227340*(349307640*x^4 + 1135249830*x^3 + 1308416040*x^2 + 646472325*x + 116
805778)/(3*x + 2)^5 + 5324/117649*ln(abs(3*x + 2)) - 5324/117649*ln(abs(2*x - 1)
)