3.1597 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=75 \[ \frac{16}{41503 (1-2 x)}-\frac{1998}{343 (3 x+2)}-\frac{625}{121 (5 x+3)}-\frac{27}{98 (3 x+2)^2}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331} \]

[Out]

16/(41503*(1 - 2*x)) - 27/(98*(2 + 3*x)^2) - 1998/(343*(2 + 3*x)) - 625/(121*(3
+ 5*x)) - (2704*Log[1 - 2*x])/3195731 + (107109*Log[2 + 3*x])/2401 - (59375*Log[
3 + 5*x])/1331

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Rubi [A]  time = 0.0861637, antiderivative size = 75, 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 \[ \frac{16}{41503 (1-2 x)}-\frac{1998}{343 (3 x+2)}-\frac{625}{121 (5 x+3)}-\frac{27}{98 (3 x+2)^2}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

16/(41503*(1 - 2*x)) - 27/(98*(2 + 3*x)^2) - 1998/(343*(2 + 3*x)) - 625/(121*(3
+ 5*x)) - (2704*Log[1 - 2*x])/3195731 + (107109*Log[2 + 3*x])/2401 - (59375*Log[
3 + 5*x])/1331

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Rubi in Sympy [A]  time = 11.4149, size = 60, normalized size = 0.8 \[ - \frac{2704 \log{\left (- 2 x + 1 \right )}}{3195731} + \frac{107109 \log{\left (3 x + 2 \right )}}{2401} - \frac{59375 \log{\left (5 x + 3 \right )}}{1331} - \frac{625}{121 \left (5 x + 3\right )} - \frac{1998}{343 \left (3 x + 2\right )} - \frac{27}{98 \left (3 x + 2\right )^{2}} + \frac{16}{41503 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2704*log(-2*x + 1)/3195731 + 107109*log(3*x + 2)/2401 - 59375*log(5*x + 3)/1331
- 625/(121*(5*x + 3)) - 1998/(343*(3*x + 2)) - 27/(98*(3*x + 2)**2) + 16/(41503
*(-2*x + 1))

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Mathematica [A]  time = 0.122507, size = 65, normalized size = 0.87 \[ \frac{-\frac{77 \left (22224420 x^3+17783592 x^2-5074951 x-4684319\right )}{(3 x+2)^2 \left (10 x^2+x-3\right )}-5408 \log (3-6 x)[phone] \log (3 x+2)-285118750 \log (-3 (5 x+3))}{6391462} \]

Antiderivative was successfully verified.

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

[Out]

((-77*(-4684319 - 5074951*x + 17783592*x^2 + 22224420*x^3))/((2 + 3*x)^2*(-3 + x
+ 10*x^2)) - 5408*Log[3 - 6*x] + 285124158*Log[2 + 3*x] - 285118750*Log[-3*(3 +
5*x)])/6391462

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Maple [A]  time = 0.018, size = 62, normalized size = 0.8 \[ -{\frac{625}{363+605\,x}}-{\frac{59375\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{27}{98\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1998}{686+1029\,x}}+{\frac{107109\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{16}{-41503+83006\,x}}-{\frac{2704\,\ln \left ( -1+2\,x \right ) }{3195731}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/121/(3+5*x)-59375/1331*ln(3+5*x)-27/98/(2+3*x)^2-1998/343/(2+3*x)+107109/24
01*ln(2+3*x)-16/41503/(-1+2*x)-2704/3195731*ln(-1+2*x)

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Maxima [A]  time = 1.3532, size = 86, normalized size = 1.15 \[ -\frac{22224420 \, x^{3} + 17783592 \, x^{2} - 5074951 \, x - 4684319}{83006 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} - \frac{59375}{1331} \, \log \left (5 \, x + 3\right ) + \frac{107109}{2401} \, \log \left (3 \, x + 2\right ) - \frac{2704}{3195731} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/83006*(22224420*x^3 + 17783592*x^2 - 5074951*x - 4684319)/(90*x^4 + 129*x^3 +
25*x^2 - 32*x - 12) - 59375/1331*log(5*x + 3) + 107109/2401*log(3*x + 2) - 2704
/3195731*log(2*x - 1)

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Fricas [A]  time = 0.217419, size = 166, normalized size = 2.21 \[ -\frac{1711280340 \, x^{3} + 1369336584 \, x^{2} + 285118750 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (5 \, x + 3\right ) - 285124158 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (3 \, x + 2\right ) + 5408 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (2 \, x - 1\right ) - 390771227 \, x - 360692563}{6391462 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6391462*(1711280340*x^3 + 1369336584*x^2 + 285118750*(90*x^4 + 129*x^3 + 25*x
^2 - 32*x - 12)*log(5*x + 3) - 285124158*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)
*log(3*x + 2) + 5408*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log(2*x - 1) - 3907
71227*x - 360692563)/(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)

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Sympy [A]  time = 0.602612, size = 65, normalized size = 0.87 \[ - \frac{22224420 x^{3} + 17783592 x^{2} - 5074951 x - 4684319}{7470540 x^{4} + 10707774 x^{3} + 2075150 x^{2} - 2656192 x - 996072} - \frac{2704 \log{\left (x - \frac{1}{2} \right )}}{3195731} - \frac{59375 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{107109 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(22224420*x**3 + 17783592*x**2 - 5074951*x - 4684319)/(7470540*x**4 + 10707774*
x**3 + 2075150*x**2 - 2656192*x - 996072) - 2704*log(x - 1/2)/3195731 - 59375*lo
g(x + 3/5)/1331 + 107109*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.211171, size = 116, normalized size = 1.55 \[ -\frac{625}{121 \,{\left (5 \, x + 3\right )}} + \frac{5 \,{\left (\frac{604065417}{5 \, x + 3} + \frac{258530842}{{\left (5 \, x + 3\right )}^{2}} - 118375902\right )}}{913066 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + \frac{107109}{2401} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{2704}{3195731} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/121/(5*x + 3) + 5/913066*(604065417/(5*x + 3) + 258530842/(5*x + 3)^2 - 118
375902)/((11/(5*x + 3) - 2)*(1/(5*x + 3) + 3)^2) + 107109/2401*ln(abs(-1/(5*x +
3) - 3)) - 2704/3195731*ln(abs(-11/(5*x + 3) + 2))