3.1627 \(\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^6} \, dx\)

Optimal. Leaf size=98 \[ \frac{2608}{823543 (1-2 x)}-\frac{7680}{823543 (3 x+2)}+\frac{88}{117649 (1-2 x)^2}-\frac{1140}{117649 (3 x+2)^2}-\frac{186}{16807 (3 x+2)^3}-\frac{87}{9604 (3 x+2)^4}+\frac{3}{1715 (3 x+2)^5}-\frac{3312 \log (1-2 x)}{823543}+\frac{3312 \log (3 x+2)}{823543} \]

[Out]

88/(117649*(1 - 2*x)^2) + 2608/(823543*(1 - 2*x)) + 3/(1715*(2 + 3*x)^5) - 87/(9
604*(2 + 3*x)^4) - 186/(16807*(2 + 3*x)^3) - 1140/(117649*(2 + 3*x)^2) - 7680/(8
23543*(2 + 3*x)) - (3312*Log[1 - 2*x])/823543 + (3312*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.113477, antiderivative size = 98, 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 \[ \frac{2608}{823543 (1-2 x)}-\frac{7680}{823543 (3 x+2)}+\frac{88}{117649 (1-2 x)^2}-\frac{1140}{117649 (3 x+2)^2}-\frac{186}{16807 (3 x+2)^3}-\frac{87}{9604 (3 x+2)^4}+\frac{3}{1715 (3 x+2)^5}-\frac{3312 \log (1-2 x)}{823543}+\frac{3312 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

88/(117649*(1 - 2*x)^2) + 2608/(823543*(1 - 2*x)) + 3/(1715*(2 + 3*x)^5) - 87/(9
604*(2 + 3*x)^4) - 186/(16807*(2 + 3*x)^3) - 1140/(117649*(2 + 3*x)^2) - 7680/(8
23543*(2 + 3*x)) - (3312*Log[1 - 2*x])/823543 + (3312*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 14.1627, size = 83, normalized size = 0.85 \[ - \frac{3312 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{3312 \log{\left (3 x + 2 \right )}}{823543} - \frac{7680}{823543 \left (3 x + 2\right )} - \frac{1140}{117649 \left (3 x + 2\right )^{2}} - \frac{186}{16807 \left (3 x + 2\right )^{3}} - \frac{87}{9604 \left (3 x + 2\right )^{4}} + \frac{3}{1715 \left (3 x + 2\right )^{5}} + \frac{2608}{823543 \left (- 2 x + 1\right )} + \frac{88}{117649 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3312*log(-2*x + 1)/823543 + 3312*log(3*x + 2)/823543 - 7680/(823543*(3*x + 2))
- 1140/(117649*(3*x + 2)**2) - 186/(16807*(3*x + 2)**3) - 87/(9604*(3*x + 2)**4)
+ 3/(1715*(3*x + 2)**5) + 2608/(823543*(-2*x + 1)) + 88/(117649*(-2*x + 1)**2)

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Mathematica [A]  time = 0.101523, size = 69, normalized size = 0.7 \[ \frac{3 \left (-\frac{7 \left (10730880 x^6+24144480 x^5+13811040 x^4-5468940 x^3-7360644 x^2-1134751 x+381394\right )}{3 (1-2 x)^2 (3 x+2)^5}-22080 \log (3-6 x)+22080 \log (3 x+2)\right )}{16470860} \]

Antiderivative was successfully verified.

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

[Out]

(3*((-7*(381394 - 1134751*x - 7360644*x^2 - 5468940*x^3 + 13811040*x^4 + 2414448
0*x^5 + 10730880*x^6))/(3*(1 - 2*x)^2*(2 + 3*x)^5) - 22080*Log[3 - 6*x] + 22080*
Log[2 + 3*x]))/16470860

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Maple [A]  time = 0.016, size = 81, normalized size = 0.8 \[{\frac{3}{1715\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{87}{9604\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{186}{16807\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1140}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{7680}{1647086+2470629\,x}}+{\frac{3312\,\ln \left ( 2+3\,x \right ) }{823543}}+{\frac{88}{117649\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{2608}{-823543+1647086\,x}}-{\frac{3312\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/1715/(2+3*x)^5-87/9604/(2+3*x)^4-186/16807/(2+3*x)^3-1140/117649/(2+3*x)^2-768
0/823543/(2+3*x)+3312/823543*ln(2+3*x)+88/117649/(-1+2*x)^2-2608/823543/(-1+2*x)
-3312/823543*ln(-1+2*x)

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Maxima [A]  time = 1.33102, size = 116, normalized size = 1.18 \[ -\frac{10730880 \, x^{6} + 24144480 \, x^{5} + 13811040 \, x^{4} - 5468940 \, x^{3} - 7360644 \, x^{2} - 1134751 \, x + 381394}{2352980 \,{\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} + \frac{3312}{823543} \, \log \left (3 \, x + 2\right ) - \frac{3312}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2352980*(10730880*x^6 + 24144480*x^5 + 13811040*x^4 - 5468940*x^3 - 7360644*x
^2 - 1134751*x + 381394)/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 11
2*x^2 + 112*x + 32) + 3312/823543*log(3*x + 2) - 3312/823543*log(2*x - 1)

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Fricas [A]  time = 0.220861, size = 209, normalized size = 2.13 \[ -\frac{75116160 \, x^{6} + 169011360 \, x^{5} + 96677280 \, x^{4} - 38282580 \, x^{3} - 51524508 \, x^{2} - 66240 \,{\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 66240 \,{\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (2 \, x - 1\right ) - 7943257 \, x + 2669758}{16470860 \,{\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/16470860*(75116160*x^6 + 169011360*x^5 + 96677280*x^4 - 38282580*x^3 - 515245
08*x^2 - 66240*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 11
2*x + 32)*log(3*x + 2) + 66240*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^
3 - 112*x^2 + 112*x + 32)*log(2*x - 1) - 7943257*x + 2669758)/(972*x^7 + 2268*x^
6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)

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Sympy [A]  time = 0.596514, size = 85, normalized size = 0.87 \[ - \frac{10730880 x^{6} + 24144480 x^{5} + 13811040 x^{4} - 5468940 x^{3} - 7360644 x^{2} - 1134751 x + 381394}{2287096560 x^{7} + 5336558640 x^{6} + 3112992540 x^{5} - 1482377400 x^{4} - 1976503200 x^{3} - 263533760 x^{2} + 263533760 x + 75295360} - \frac{3312 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{3312 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(10730880*x**6 + 24144480*x**5 + 13811040*x**4 - 5468940*x**3 - 7360644*x**2 -
1134751*x + 381394)/(2287096560*x**7 + 5336558640*x**6 + 3112992540*x**5 - 14823
77400*x**4 - 1976503200*x**3 - 263533760*x**2 + 263533760*x + 75295360) - 3312*l
og(x - 1/2)/823543 + 3312*log(x + 2/3)/823543

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GIAC/XCAS [A]  time = 0.206237, size = 88, normalized size = 0.9 \[ -\frac{10730880 \, x^{6} + 24144480 \, x^{5} + 13811040 \, x^{4} - 5468940 \, x^{3} - 7360644 \, x^{2} - 1134751 \, x + 381394}{2352980 \,{\left (3 \, x + 2\right )}^{5}{\left (2 \, x - 1\right )}^{2}} + \frac{3312}{823543} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{3312}{823543} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2352980*(10730880*x^6 + 24144480*x^5 + 13811040*x^4 - 5468940*x^3 - 7360644*x
^2 - 1134751*x + 381394)/((3*x + 2)^5*(2*x - 1)^2) + 3312/823543*ln(abs(3*x + 2)
) - 3312/823543*ln(abs(2*x - 1))