3.1611 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=86 \[ \frac{32}{456533 (1-2 x)}+\frac{8829}{343 (3 x+2)}+\frac{59375}{1331 (5 x+3)}+\frac{81}{98 (3 x+2)^2}-\frac{625}{242 (5 x+3)^2}-\frac{6528 \log (1-2 x)}{35153041}-\frac{630342 \log (3 x+2)}{2401}+\frac{3843750 \log (5 x+3)}{14641} \]

[Out]

32/(456533*(1 - 2*x)) + 81/(98*(2 + 3*x)^2) + 8829/(343*(2 + 3*x)) - 625/(242*(3
+ 5*x)^2) + 59375/(1331*(3 + 5*x)) - (6528*Log[1 - 2*x])/35153041 - (630342*Log
[2 + 3*x])/2401 + (3843750*Log[3 + 5*x])/14641

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Rubi [A]  time = 0.103539, antiderivative size = 86, 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 \[ \frac{32}{456533 (1-2 x)}+\frac{8829}{343 (3 x+2)}+\frac{59375}{1331 (5 x+3)}+\frac{81}{98 (3 x+2)^2}-\frac{625}{242 (5 x+3)^2}-\frac{6528 \log (1-2 x)}{35153041}-\frac{630342 \log (3 x+2)}{2401}+\frac{3843750 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

32/(456533*(1 - 2*x)) + 81/(98*(2 + 3*x)^2) + 8829/(343*(2 + 3*x)) - 625/(242*(3
+ 5*x)^2) + 59375/(1331*(3 + 5*x)) - (6528*Log[1 - 2*x])/35153041 - (630342*Log
[2 + 3*x])/2401 + (3843750*Log[3 + 5*x])/14641

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Rubi in Sympy [A]  time = 12.9254, size = 70, normalized size = 0.81 \[ - \frac{6528 \log{\left (- 2 x + 1 \right )}}{35153041} - \frac{630342 \log{\left (3 x + 2 \right )}}{2401} + \frac{3843750 \log{\left (5 x + 3 \right )}}{14641} + \frac{59375}{1331 \left (5 x + 3\right )} - \frac{625}{242 \left (5 x + 3\right )^{2}} + \frac{8829}{343 \left (3 x + 2\right )} + \frac{81}{98 \left (3 x + 2\right )^{2}} + \frac{32}{456533 \left (- 2 x + 1\right )} \]

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)**3,x)

[Out]

-6528*log(-2*x + 1)/35153041 - 630342*log(3*x + 2)/2401 + 3843750*log(5*x + 3)/1
4641 + 59375/(1331*(5*x + 3)) - 625/(242*(5*x + 3)**2) + 8829/(343*(3*x + 2)) +
81/(98*(3*x + 2)**2) + 32/(456533*(-2*x + 1))

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Mathematica [A]  time = 0.180864, size = 79, normalized size = 0.92 \[ \frac{2 \left (\frac{77}{4} \left (\frac{23502798}{3 x+2}+\frac{40731250}{5 x+3}+\frac{754677}{(3 x+2)^2}-\frac{2358125}{(5 x+3)^2}+\frac{64}{1-2 x}\right )-3264 \log (1-2 x)-4614418611 \log (6 x+4)[phone] \log (10 x+6)\right )}{35153041} \]

Antiderivative was successfully verified.

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

[Out]

(2*((77*(64/(1 - 2*x) + 754677/(2 + 3*x)^2 + 23502798/(2 + 3*x) - 2358125/(3 + 5
*x)^2 + 40731250/(3 + 5*x)))/4 - 3264*Log[1 - 2*x] - 4614418611*Log[4 + 6*x] + 4
614421875*Log[6 + 10*x]))/35153041

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Maple [A]  time = 0.021, size = 71, normalized size = 0.8 \[ -{\frac{625}{242\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{59375}{3993+6655\,x}}+{\frac{3843750\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{81}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8829}{686+1029\,x}}-{\frac{630342\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{32}{-456533+913066\,x}}-{\frac{6528\,\ln \left ( -1+2\,x \right ) }{35153041}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/242/(3+5*x)^2+59375/1331/(3+5*x)+3843750/14641*ln(3+5*x)+81/98/(2+3*x)^2+88
29/343/(2+3*x)-630342/2401*ln(2+3*x)-32/456533/(-1+2*x)-6528/35153041*ln(-1+2*x)

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Maxima [A]  time = 1.35165, size = 100, normalized size = 1.16 \[ \frac{7191217800 \, x^{4} + 10067655960 \, x^{3} + 1808383578 \, x^{2} - 2501680914 \, x - 909187261}{913066 \,{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )}} + \frac{3843750}{14641} \, \log \left (5 \, x + 3\right ) - \frac{630342}{2401} \, \log \left (3 \, x + 2\right ) - \frac{6528}{35153041} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/913066*(7191217800*x^4 + 10067655960*x^3 + 1808383578*x^2 - 2501680914*x - 909
187261)/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36) + 3843750/14641*log(
5*x + 3) - 630342/2401*log(3*x + 2) - 6528/35153041*log(2*x - 1)

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Fricas [A]  time = 0.221154, size = 200, normalized size = 2.33 \[ \frac{553723770600 \, x^{4} + 775209508920 \, x^{3} + 139245535506 \, x^{2} + 18457687500 \,{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (5 \, x + 3\right ) - 18457674444 \,{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (3 \, x + 2\right ) - 13056 \,{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (2 \, x - 1\right ) - 192629430378 \, x - 70007419097}{70306082 \,{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/70306082*(553723770600*x^4 + 775209508920*x^3 + 139245535506*x^2 + 18457687500
*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(5*x + 3) - 18457674444*
(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(3*x + 2) - 13056*(450*x^
5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(2*x - 1) - 192629430378*x - 700
07419097)/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)

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Sympy [A]  time = 0.655068, size = 75, normalized size = 0.87 \[ \frac{7191217800 x^{4} + 10067655960 x^{3} + 1808383578 x^{2} - 2501680914 x - 909187261}{410879700 x^{5} + 835455390 x^{4} + 467489792 x^{3} - 77610610 x^{2} - 142438296 x - 32870376} - \frac{6528 \log{\left (x - \frac{1}{2} \right )}}{35153041} + \frac{3843750 \log{\left (x + \frac{3}{5} \right )}}{14641} - \frac{630342 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(7191217800*x**4 + 10067655960*x**3 + 1808383578*x**2 - 2501680914*x - 909187261
)/(410879700*x**5 + 835455390*x**4 + 467489792*x**3 - 77610610*x**2 - 142438296*
x - 32870376) - 6528*log(x - 1/2)/35153041 + 3843750*log(x + 3/5)/14641 - 630342
*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.213745, size = 131, normalized size = 1.52 \[ -\frac{32}{456533 \,{\left (2 \, x - 1\right )}} - \frac{4 \,{\left (\frac{207724651275}{2 \, x - 1} + \frac{470659858850}{{\left (2 \, x - 1\right )}^{2}} + \frac{355299675423}{{\left (2 \, x - 1\right )}^{3}} + 30544881750\right )}}{35153041 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} - \frac{630342}{2401} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{3843750}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-32/456533/(2*x - 1) - 4/35153041*(207724651275/(2*x - 1) + 470659858850/(2*x -
1)^2 + 355299675423/(2*x - 1)^3 + 30544881750)/((11/(2*x - 1) + 5)^2*(7/(2*x - 1
) + 3)^2) - 630342/2401*ln(abs(-7/(2*x - 1) - 3)) + 3843750/14641*ln(abs(-11/(2*
x - 1) - 5))