3.1582 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=64 \[ \frac{8}{3773 (1-2 x)}+\frac{351}{343 (3 x+2)}+\frac{9}{98 (3 x+2)^2}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3) \]

[Out]

8/(3773*(1 - 2*x)) + 9/(98*(2 + 3*x)^2) + 351/(343*(2 + 3*x)) - (1072*Log[1 - 2*
x])/290521 - (12393*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/121

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Rubi [A]  time = 0.0738582, antiderivative size = 64, 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 \[ \frac{8}{3773 (1-2 x)}+\frac{351}{343 (3 x+2)}+\frac{9}{98 (3 x+2)^2}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

8/(3773*(1 - 2*x)) + 9/(98*(2 + 3*x)^2) + 351/(343*(2 + 3*x)) - (1072*Log[1 - 2*
x])/290521 - (12393*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/121

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Rubi in Sympy [A]  time = 10.1114, size = 53, normalized size = 0.83 \[ - \frac{1072 \log{\left (- 2 x + 1 \right )}}{290521} - \frac{12393 \log{\left (3 x + 2 \right )}}{2401} + \frac{625 \log{\left (5 x + 3 \right )}}{121} + \frac{351}{343 \left (3 x + 2\right )} + \frac{9}{98 \left (3 x + 2\right )^{2}} + \frac{8}{3773 \left (- 2 x + 1\right )} \]

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),x)

[Out]

-1072*log(-2*x + 1)/290521 - 12393*log(3*x + 2)/2401 + 625*log(5*x + 3)/121 + 35
1/(343*(3*x + 2)) + 9/(98*(3*x + 2)**2) + 8/(3773*(-2*x + 1))

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Mathematica [A]  time = 0.0812309, size = 61, normalized size = 0.95 \[ \frac{-2144 \log (5-10 x)-2999106 \log (5 (3 x+2))+7 \left (\frac{176}{1-2 x}+\frac{84942}{3 x+2}+\frac{7623}{(3 x+2)^2}+428750 \log (5 x+3)\right )}{581042} \]

Antiderivative was successfully verified.

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

[Out]

(-2144*Log[5 - 10*x] - 2999106*Log[5*(2 + 3*x)] + 7*(176/(1 - 2*x) + 7623/(2 + 3
*x)^2 + 84942/(2 + 3*x) + 428750*Log[3 + 5*x]))/581042

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Maple [A]  time = 0.017, size = 53, normalized size = 0.8 \[{\frac{625\,\ln \left ( 3+5\,x \right ) }{121}}+{\frac{9}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{351}{686+1029\,x}}-{\frac{12393\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{8}{-3773+7546\,x}}-{\frac{1072\,\ln \left ( -1+2\,x \right ) }{290521}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

625/121*ln(3+5*x)+9/98/(2+3*x)^2+351/343/(2+3*x)-12393/2401*ln(2+3*x)-8/3773/(-1
+2*x)-1072/290521*ln(-1+2*x)

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Maxima [A]  time = 1.35941, size = 73, normalized size = 1.14 \[ \frac{46188 \, x^{2} + 8916 \, x - 16201}{7546 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac{625}{121} \, \log \left (5 \, x + 3\right ) - \frac{12393}{2401} \, \log \left (3 \, x + 2\right ) - \frac{1072}{290521} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7546*(46188*x^2 + 8916*x - 16201)/(18*x^3 + 15*x^2 - 4*x - 4) + 625/121*log(5*
x + 3) - 12393/2401*log(3*x + 2) - 1072/290521*log(2*x - 1)

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Fricas [A]  time = 0.218033, size = 132, normalized size = 2.06 \[ \frac{3556476 \, x^{2} + 3001250 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (5 \, x + 3\right ) - 2999106 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 2144 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 686532 \, x - 1247477}{581042 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/581042*(3556476*x^2 + 3001250*(18*x^3 + 15*x^2 - 4*x - 4)*log(5*x + 3) - 29991
06*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) - 2144*(18*x^3 + 15*x^2 - 4*x - 4)*l
og(2*x - 1) + 686532*x - 1247477)/(18*x^3 + 15*x^2 - 4*x - 4)

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Sympy [A]  time = 0.531974, size = 54, normalized size = 0.84 \[ \frac{46188 x^{2} + 8916 x - 16201}{135828 x^{3} + 113190 x^{2} - 30184 x - 30184} - \frac{1072 \log{\left (x - \frac{1}{2} \right )}}{290521} + \frac{625 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{12393 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(46188*x**2 + 8916*x - 16201)/(135828*x**3 + 113190*x**2 - 30184*x - 30184) - 10
72*log(x - 1/2)/290521 + 625*log(x + 3/5)/121 - 12393*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.209883, size = 89, normalized size = 1.39 \[ -\frac{8}{3773 \,{\left (2 \, x - 1\right )}} - \frac{54 \,{\left (\frac{287}{2 \, x - 1} + 120\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} - \frac{12393}{2401} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{625}{121} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/3773/(2*x - 1) - 54/2401*(287/(2*x - 1) + 120)/(7/(2*x - 1) + 3)^2 - 12393/24
01*ln(abs(-7/(2*x - 1) - 3)) + 625/121*ln(abs(-11/(2*x - 1) - 5))