3.1583 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=75 \[ \frac{16}{26411 (1-2 x)}+\frac{12393}{2401 (3 x+2)}+\frac{351}{686 (3 x+2)^2}+\frac{3}{49 (3 x+2)^3}-\frac{2672 \log (1-2 x)}{2033647}-\frac{434043 \log (3 x+2)}{16807}+\frac{3125}{121} \log (5 x+3) \]

[Out]

16/(26411*(1 - 2*x)) + 3/(49*(2 + 3*x)^3) + 351/(686*(2 + 3*x)^2) + 12393/(2401*
(2 + 3*x)) - (2672*Log[1 - 2*x])/2033647 - (434043*Log[2 + 3*x])/16807 + (3125*L
og[3 + 5*x])/121

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Rubi [A]  time = 0.0888468, 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 \[ \frac{16}{26411 (1-2 x)}+\frac{12393}{2401 (3 x+2)}+\frac{351}{686 (3 x+2)^2}+\frac{3}{49 (3 x+2)^3}-\frac{2672 \log (1-2 x)}{2033647}-\frac{434043 \log (3 x+2)}{16807}+\frac{3125}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

16/(26411*(1 - 2*x)) + 3/(49*(2 + 3*x)^3) + 351/(686*(2 + 3*x)^2) + 12393/(2401*
(2 + 3*x)) - (2672*Log[1 - 2*x])/2033647 - (434043*Log[2 + 3*x])/16807 + (3125*L
og[3 + 5*x])/121

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Rubi in Sympy [A]  time = 11.4838, size = 63, normalized size = 0.84 \[ - \frac{2672 \log{\left (- 2 x + 1 \right )}}{2033647} - \frac{434043 \log{\left (3 x + 2 \right )}}{16807} + \frac{3125 \log{\left (5 x + 3 \right )}}{121} + \frac{12393}{2401 \left (3 x + 2\right )} + \frac{351}{686 \left (3 x + 2\right )^{2}} + \frac{3}{49 \left (3 x + 2\right )^{3}} + \frac{16}{26411 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1-2*x)**2/(2+3*x)**4/(3+5*x),x)

[Out]

-2672*log(-2*x + 1)/2033647 - 434043*log(3*x + 2)/16807 + 3125*log(5*x + 3)/121
+ 12393/(2401*(3*x + 2)) + 351/(686*(3*x + 2)**2) + 3/(49*(3*x + 2)**3) + 16/(26
411*(-2*x + 1))

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Mathematica [A]  time = 0.0934475, size = 70, normalized size = 0.93 \[ \frac{77 \left (\frac{272646}{3 x+2}+\frac{27027}{(3 x+2)^2}+\frac{3234}{(3 x+2)^3}+\frac{32}{1-2 x}\right )-5344 \log (5-10 x)-105038406 \log (5 (3 x+2))[phone] \log (5 x+3)}{4067294} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

(77*(32/(1 - 2*x) + 3234/(2 + 3*x)^3 + 27027/(2 + 3*x)^2 + 272646/(2 + 3*x)) - 5
344*Log[5 - 10*x] - 105038406*Log[5*(2 + 3*x)] + 105043750*Log[3 + 5*x])/4067294

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Maple [A]  time = 0.017, size = 62, normalized size = 0.8 \[{\frac{3125\,\ln \left ( 3+5\,x \right ) }{121}}+{\frac{3}{49\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{351}{686\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{12393}{4802+7203\,x}}-{\frac{434043\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{16}{-26411+52822\,x}}-{\frac{2672\,\ln \left ( -1+2\,x \right ) }{2033647}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^2/(2+3*x)^4/(3+5*x),x)

[Out]

3125/121*ln(3+5*x)+3/49/(2+3*x)^3+351/686/(2+3*x)^2+12393/2401/(2+3*x)-434043/16
807*ln(2+3*x)-16/26411/(-1+2*x)-2672/2033647*ln(-1+2*x)

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Maxima [A]  time = 1.35754, size = 86, normalized size = 1.15 \[ \frac{4906764 \, x^{3} + 4250124 \, x^{2} - 1058241 \, x - 1148128}{52822 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{3125}{121} \, \log \left (5 \, x + 3\right ) - \frac{434043}{16807} \, \log \left (3 \, x + 2\right ) - \frac{2672}{2033647} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")

[Out]

1/52822*(4906764*x^3 + 4250124*x^2 - 1058241*x - 1148128)/(54*x^4 + 81*x^3 + 18*
x^2 - 20*x - 8) + 3125/121*log(5*x + 3) - 434043/16807*log(3*x + 2) - 2672/20336
47*log(2*x - 1)

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Fricas [A]  time = 0.216579, size = 166, normalized size = 2.21 \[ \frac{377820828 \, x^{3} + 327259548 \, x^{2} + 105043750 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (5 \, x + 3\right ) - 105038406 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) - 5344 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) - 81484557 \, x - 88405856}{4067294 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/4067294*(377820828*x^3 + 327259548*x^2 + 105043750*(54*x^4 + 81*x^3 + 18*x^2 -
20*x - 8)*log(5*x + 3) - 105038406*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(3*
x + 2) - 5344*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) - 81484557*x -
88405856)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)

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Sympy [A]  time = 0.587477, size = 65, normalized size = 0.87 \[ \frac{4906764 x^{3} + 4250124 x^{2} - 1058241 x - 1148128}{2852388 x^{4} + 4278582 x^{3} + 950796 x^{2} - 1056440 x - 422576} - \frac{2672 \log{\left (x - \frac{1}{2} \right )}}{2033647} + \frac{3125 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{434043 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-2*x)**2/(2+3*x)**4/(3+5*x),x)

[Out]

(4906764*x**3 + 4250124*x**2 - 1058241*x - 1148128)/(2852388*x**4 + 4278582*x**3
+ 950796*x**2 - 1056440*x - 422576) - 2672*log(x - 1/2)/2033647 + 3125*log(x +
3/5)/121 - 434043*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.215436, size = 101, normalized size = 1.35 \[ -\frac{16}{26411 \,{\left (2 \, x - 1\right )}} - \frac{54 \,{\left (\frac{60375}{2 \, x - 1} + \frac{71491}{{\left (2 \, x - 1\right )}^{2}} + 12756\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} - \frac{434043}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{3125}{121} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")

[Out]

-16/26411/(2*x - 1) - 54/16807*(60375/(2*x - 1) + 71491/(2*x - 1)^2 + 12756)/(7/
(2*x - 1) + 3)^3 - 434043/16807*ln(abs(-7/(2*x - 1) - 3)) + 3125/121*ln(abs(-11/
(2*x - 1) - 5))