3.1626 \(\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^5} \, dx\)

Optimal. Leaf size=87 \[ \frac{1040}{117649 (1-2 x)}-\frac{2280}{117649 (3 x+2)}+\frac{44}{16807 (1-2 x)^2}-\frac{279}{16807 (3 x+2)^2}-\frac{29}{2401 (3 x+2)^3}+\frac{3}{1372 (3 x+2)^4}-\frac{7680 \log (1-2 x)}{823543}+\frac{7680 \log (3 x+2)}{823543} \]

[Out]

44/(16807*(1 - 2*x)^2) + 1040/(117649*(1 - 2*x)) + 3/(1372*(2 + 3*x)^4) - 29/(24
01*(2 + 3*x)^3) - 279/(16807*(2 + 3*x)^2) - 2280/(117649*(2 + 3*x)) - (7680*Log[
1 - 2*x])/823543 + (7680*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.0968173, antiderivative size = 87, 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 \[ \frac{1040}{117649 (1-2 x)}-\frac{2280}{117649 (3 x+2)}+\frac{44}{16807 (1-2 x)^2}-\frac{279}{16807 (3 x+2)^2}-\frac{29}{2401 (3 x+2)^3}+\frac{3}{1372 (3 x+2)^4}-\frac{7680 \log (1-2 x)}{823543}+\frac{7680 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

44/(16807*(1 - 2*x)^2) + 1040/(117649*(1 - 2*x)) + 3/(1372*(2 + 3*x)^4) - 29/(24
01*(2 + 3*x)^3) - 279/(16807*(2 + 3*x)^2) - 2280/(117649*(2 + 3*x)) - (7680*Log[
1 - 2*x])/823543 + (7680*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 12.5907, size = 73, normalized size = 0.84 \[ - \frac{7680 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{7680 \log{\left (3 x + 2 \right )}}{823543} - \frac{2280}{117649 \left (3 x + 2\right )} - \frac{279}{16807 \left (3 x + 2\right )^{2}} - \frac{29}{2401 \left (3 x + 2\right )^{3}} + \frac{3}{1372 \left (3 x + 2\right )^{4}} + \frac{1040}{117649 \left (- 2 x + 1\right )} + \frac{44}{16807 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7680*log(-2*x + 1)/823543 + 7680*log(3*x + 2)/823543 - 2280/(117649*(3*x + 2))
- 279/(16807*(3*x + 2)**2) - 29/(2401*(3*x + 2)**3) + 3/(1372*(3*x + 2)**4) + 10
40/(117649*(-2*x + 1)) + 44/(16807*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0913177, size = 64, normalized size = 0.74 \[ \frac{4 \left (-\frac{7 \left (1658880 x^5+2626560 x^4+384000 x^3-1101440 x^2-403584 x+28275\right )}{16 (1-2 x)^2 (3 x+2)^4}-1920 \log (1-2 x)+1920 \log (6 x+4)\right )}{823543} \]

Antiderivative was successfully verified.

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

[Out]

(4*((-7*(28275 - 403584*x - 1101440*x^2 + 384000*x^3 + 2626560*x^4 + 1658880*x^5
))/(16*(1 - 2*x)^2*(2 + 3*x)^4) - 1920*Log[1 - 2*x] + 1920*Log[4 + 6*x]))/823543

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Maple [A]  time = 0.017, size = 72, normalized size = 0.8 \[{\frac{3}{1372\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{29}{2401\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{279}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2280}{235298+352947\,x}}+{\frac{7680\,\ln \left ( 2+3\,x \right ) }{823543}}+{\frac{44}{16807\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{1040}{-117649+235298\,x}}-{\frac{7680\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/1372/(2+3*x)^4-29/2401/(2+3*x)^3-279/16807/(2+3*x)^2-2280/117649/(2+3*x)+7680/
823543*ln(2+3*x)+44/16807/(-1+2*x)^2-1040/117649/(-1+2*x)-7680/823543*ln(-1+2*x)

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Maxima [A]  time = 1.35338, size = 103, normalized size = 1.18 \[ -\frac{1658880 \, x^{5} + 2626560 \, x^{4} + 384000 \, x^{3} - 1101440 \, x^{2} - 403584 \, x + 28275}{470596 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} + \frac{7680}{823543} \, \log \left (3 \, x + 2\right ) - \frac{7680}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/470596*(1658880*x^5 + 2626560*x^4 + 384000*x^3 - 1101440*x^2 - 403584*x + 282
75)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16) + 7680/823543*l
og(3*x + 2) - 7680/823543*log(2*x - 1)

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Fricas [A]  time = 0.217427, size = 182, normalized size = 2.09 \[ -\frac{11612160 \, x^{5} + 18385920 \, x^{4} + 2688000 \, x^{3} - 7710080 \, x^{2} - 30720 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 30720 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (2 \, x - 1\right ) - 2825088 \, x + 197925}{3294172 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3294172*(11612160*x^5 + 18385920*x^4 + 2688000*x^3 - 7710080*x^2 - 30720*(324
*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(3*x + 2) + 30720*(3
24*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(2*x - 1) - 282508
8*x + 197925)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)

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Sympy [A]  time = 0.545834, size = 75, normalized size = 0.86 \[ - \frac{1658880 x^{5} + 2626560 x^{4} + 384000 x^{3} - 1101440 x^{2} - 403584 x + 28275}{152473104 x^{6} + 254121840 x^{5} + 38118276 x^{4} - 124237344 x^{3} - 48941984 x^{2} + 15059072 x + 7529536} - \frac{7680 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{7680 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1658880*x**5 + 2626560*x**4 + 384000*x**3 - 1101440*x**2 - 403584*x + 28275)/(
152473104*x**6 + 254121840*x**5 + 38118276*x**4 - 124237344*x**3 - 48941984*x**2
+ 15059072*x + 7529536) - 7680*log(x - 1/2)/823543 + 7680*log(x + 2/3)/823543

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GIAC/XCAS [A]  time = 0.209523, size = 105, normalized size = 1.21 \[ -\frac{2280}{117649 \,{\left (3 \, x + 2\right )}} + \frac{48 \,{\left (\frac{1141}{3 \, x + 2} - 293\right )}}{823543 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} - \frac{279}{16807 \,{\left (3 \, x + 2\right )}^{2}} - \frac{29}{2401 \,{\left (3 \, x + 2\right )}^{3}} + \frac{3}{1372 \,{\left (3 \, x + 2\right )}^{4}} - \frac{7680}{823543} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2280/117649/(3*x + 2) + 48/823543*(1141/(3*x + 2) - 293)/(7/(3*x + 2) - 2)^2 -
279/16807/(3*x + 2)^2 - 29/2401/(3*x + 2)^3 + 3/1372/(3*x + 2)^4 - 7680/823543*l
n(abs(-7/(3*x + 2) + 2))